Books That Help With Linear Algebra

Books That Help With Linear AlgebraLearning the basics of linear algebra is very important for most people. You will need to be able to use algebra and other forms of mathematical equations to solve problems in your everyday life. Many individuals also want to go beyond the basics of algebra so they can begin to use more advanced concepts like transcendental numbers and differential equations. Understanding these basics of linear algebra will allow you to go on to find out how to get involved in more advanced math problems.Before you even begin using algebra, you should learn a simple form of it. To do this, you will need to memorize the basics of linear algebra. The first form of this is by using addition and subtraction. Using additions and subtractions will enable you to represent numbers as a sum and a difference. This will allow you to multiply and divide numbers in your head.To figure out linear equations, you will need to take each number and match it up with the corresponding equation. For example, let's say you want to figure out the area of a square. You would start by figuring out how many times your square has to be divided by its sides. Then multiply that number by itself to find the number of times it needs to be multiplied by itself. Finally, add the results together to get the answer.Now you know the basic of it, you can start to use it. As you begin to solve linear equations in your head, you will learn about limits. Limits are situations where a term cannot be added to itself. The most common limit is known as the maximum of a linear equation. There are several other limits as well. Limits are the building blocks of most of the more complex mathematical equations.There are also some mathematical equations where there are solutions. Solving a linear equation in a straight line can be accomplished using derivatives. These are useful when you need to change one value of a derivative to another. Derivatives are useful in solving more complicated e quations as well.One of the more important limiting equations in linear algebra is known as the limit theorem. It will enable you to find out what will happen if you increase one of the variables. In addition, it will also let you know what will happen if you decrease one of the variables. In this way, you will be able to do things like solve differential equations or solve quadratic equations.Reading about linear algebra is not only fun but it will help you do more in your everyday life. Learning the basics of linear algebra will let you solve problems and get more out of mathematics.

A Guide to Personal Trainer Marketing

A Guide to Personal Trainer Marketing How to Market Yourself to Become a Personal Trainer ChaptersSimple Tips to Improve Your Marketing Strategy and Grow Your Business as a Fitness InstructorLearning About “Personal Branding” for your Personal Training BusinessLearn Search Engine Optimisation to Improve Your Digital Marketing StrategiesFind Strategic Partners to Boost Awareness of Your ProductSet Up a Referral Rewards Marketing CampaignEncourage Client Fidelity With Promotional OffersOnly too often, we imagine personal trainers as the big, muscle-bound type with inflated muscles, popping steroids and protein pills to butch up…Reality is another story: a personal trainer is in the wellness business, using his or her specific knowledge and skill sets to motivate their client, support them physically and emotionally and help them achieve their fitness goals.A personal fitness instructor is there to guide their clients toward self-fulfilment and helps them accomplish what they set out to do.Come to think of it, you could do with a few clients to guide and help, couldn†™t you? Having clients is a basic requirement when starting a personal training business.Superprof’s mini-guide to establishing yourself as a home fitness trainer is here to help you with the marketing strategies and networking tactics to help you establish a client base get your new business on its feet.share a space. You can also ask existing studios if you can rent their space - saving on some equipment costs - or if a fitness centre will let you work with private clients on their premises.Also discover what certifications personal trainers need to have...Even if it’s just a one-day event as part of their summer cookout, these are potential new clients just waiting to hear of your existence!Also look for influential partners with a large clientele of their own who would be likely to recommend you to people looking for a personal trainer - doctors, pharmacists, sports shops, real estate agents… Offer them a free session so they can tell their own clients all about you - and who knows, maybe you’ll gain a GP or a pharmacist as a client as well.You may also consider setting up a profile with Superprof. Superprof is a platform that specialises in helping to find jobs for ex teachers!Set Up a Referral Rewards Marketing CampaignOffer reduced rates or other promotional goodies (a free exercise mat, for example) to clients who recommend you to friends or family. A small business owner thrives on word-of-mouth, so make a referral rewards program part of your strategic marketing plan.Encourage clients to write testimonials for your website or post them on social media. You can sponsor contests through Facebook in which people enter by commenting or sharing your post.Encourage Client Fidelity With Promotional OffersOne universal adage of marketing is that it costs five times less to keep a client than to acquire a new one.So take good care of your loyal clientele!Some tips for rewarding loyal clientsThink about a rewards program for those who stick with you. A discount on a ten-session stamp card, for example; or you could offer little keychains or, even better, a step counter with your name on it so they think of you wherever they go.Take an example from this coffee shop - offer rewards to loyal customers of your personal trainer business. Photo credit: duncan on Visual HuntConsider an upgrade to “gold client” after three years, with discounts, free access to your exercise videos or a free nutrition consultation.Have a yearly client party so your clients meet new people and understand that you value their loyalty.Keeping Your Clients Outside of Marketing ChannelsEffective marketing aside, don’t forget that your clients are people and that the best way to keep them is to take care of them.Try to be flexible with scheduling and understanding of last-minute emergencies. Take the time to get to know them and adapt their personal training to their skills and needs.During a training session:Be kind and attentiveBe sympathetic - getting stress factors out in the open will give them a sense of release and allow them to concentrate on their trainingBe aware of what your client is saying - both out loud and with their body. Stress might be evident through tense muscles, tiredness through disjointed sentences.Make sure the workout stays safe and that they don’t injure themselves because they didn’t realise how stressed-out they really were.Create a calm atmosphere: use music or simply speak in a calm and measured voiceCreate an atmosphere of trust: call them by their first name, be cheerful and make small talkEncourage them and motivate them when they are experiencing difficultiesPraise them when they make progressThese simple strategies will help you grow and keep new clients. Superprof is ready to play its part in getting you known!Now discover this beginner's guide to being a personal trainer...

What is it Like to Attend The CUNY College of Staten Island

What is it Like to Attend The CUNY College of Staten Island The tutors behind Varsity Tutors are not just here to teach theyre sharing their college experiences as well. Maria graduated from The CUNY (City University of New York) College of Staten Island in 2012 with a degree in History. She is currently New York City tutor specializing in Phonics tutoring, Spanish tutoring, World History tutoring, and more. See what she had to say about her alma mater: VT: Describe the campus setting and transportation options.How urban or safe is the campus?Are there buses or do you need a car/bike? Maria: The campus is set off of Victory Boulevard, which is one of the main streets in Staten Island. Therefore, there are many options to use public transportation from different areas of all five boroughs and a short drive from the NY/NJ border. There are two entrances into the college. There is the main entrance on Victory Boulevard, and the south entrance which is easily accessible by public transportation. A student can also ride their bike into campus, and secure it near the library. There are express buses that drive to the entrance of the college, a FREE shuttle that picks up students from the Staten Island Ferry and drops them off inside of the campus, an internal bus service within the campus grounds, and a bus that comes from Bay Ridge, Brooklyn. The campus is extremely safe with many public safety officers in almost every building, especially in the Campus Center, the administration buildings, and the library. VT: How available are the professors, academic advisers, and teaching assistants? Maria: Professors, academic advisors, and teaching assistants are readily available in person, with or without an appointment, and most conveniently by email. Most professors are available before and after class for any questions regarding course material and assignments. Advisors are available anytime throughout the year, and are extremely knowledgeable. VT: How would you describe the dorm life rooms, dining options, location, socialization opportunities with other students? Maria: Dorms will make their grand debut beginning this coming fall semester (2013), therefore, I have no direct experience concerning dorm life. However, the establishment is going to be very spacious with suites that contain even up to 4 bedrooms. There are many opportunities for socialization, with two cafes and a restaurant available on campus. There are also many student activities such as clubs, a radio station on campus, student leadership development programs, study-abroad opportunities, and many other opportunities to travel the country and the world. The campus is smoke-free, eco-friendly, and even has a garden, a college newspaper and a journal. VT: Which majors/programs are best represented and supported?What did you study and why? Did the university do a good job supporting your particular area of study? Maria: I obtained a Bachelor's Degree in History, in which The College of Staten Island did a great job in supporting my academic career. I received academic advisement and counseling throughout the year, and many advisors and professors were readily available. The college has many programs from Associates Degree to Doctoral programs. They are well-known for their Education, Finance, Biology, Chemistry, Social Work, Accounting, History, Philosophy, Astronomy, African Studies, Sociology, Psychology, Nursing, and Media-Communications departments. VT: How easy or difficult was it for you to meet people and make friends as a freshman? Does Greek life play a significant role in the campus social life? Maria: It was extremely easy for my to make friends my freshman year in college. Students are extremely approachable and your best tools to socialize are clubs and Greek Life on campus. Greek Life is active on campus. They even have clubs. They also participate in charity work and other fundraisers. VT: How helpful is the Career Centerand other student support services?Do many reputable companies recruit on campus? Maria: The Career Center is extremely helpful and helped me find a work-study program that best suited my needs and interests. There are also many employment opportunities available through the college such as the Teaching Scholars program, work-study program, and Liberty Partnership. The college also hires students as tutors. Many reputable companies from city jobs and other highly-recognized organizations recruit from job fairs which are held on campus. VT: How are the various study areas such aslibraries, student union, and dorm lounges?Are they over-crowded, easily available, spacious? Maria: The library, Campus Center, Green Dolphin Lounge, and Sleeping Dolphin Lounge are each unique in their own ways. The library has floors designated for different sound levels. The first floor is designated for normal socializing, all the way to the fourth floor, which is completely silent and regulated by public safety officers. The Campus Center is where all the clubs meet, and where Student Life offices and conference rooms are located. The Sleeping Dolphin Lounge is designated for those who need a power nap before, in between, or after classes, and the Green Dolphin Lounge provides refreshments, a spacious sitting area with tables and couches, along with a mini-cafe that is open when movies are being shown. VT: Describe the surrounding town. What kinds of outside establishments / things to do are there that make it fun, boring, or somewhere in between?To what extent do students go to the downtown area of the city versus staying near campus? Maria: There is a mall, various shopping centers, and diverse restaurants located near the college. There are also bowling alleys, a public library, and Manhattan is about 30 minutes away via public transportation. New Jersey is also a ten-minute car ride away from the college. The Jersey Shore is about 30-45 minutes away (by car) from campus. In the surrounding area, there are also buses that ride to Atlantic City (casinos, boardwalk, etc.). VT: How big or small is the student body? Were you generally pleased or displeased with the typical class sizes? Maria: The student body is made up of a few thousand students, taking classes throughout the day. As of right now, they are all commuter students, however, I do not know what their prospective student population will be once they open their dorms. Class sizes vary from 10 students in a class, to 150-200 students in a class. Class sizes vary depending on the academic level of the course, and if it is a lecture or not. VT: Describe one memorable experience with a professor and/or class. Perhaps one you loved the most or one youregretthe most. Maria: Every experience has been pleasant except for one. But the experience I loved the most was with my senior thesis professor who guided me and was an immense help when I was writing my final thesis. She helped me acquire resources and helped me in the beginning. She gave me the advice and confidence to help myself be able to complete my 35-page thesis at the end of the semester with confidence and efficiency. Check out Marias tutoring profile. The views expressed in this article do not necessarily represent the views of Varsity Tutors.

Online Factor Tree Tutors

Online Factor Tree Tutors Factor tree is a tool which is used to find out the factorization with the help of factorization methods. Like tree has many branches, in the similar way it is required to solve factorization problems in various steps. Tree basically resembles the factorization steps which generally step by step procedure. It not only factorizes the expression but it also helps in solving the equations. Question 1:- Factor and solve the following expression: - x^2 + 14x+ 48= 0 Solution 1:- In this question given expression is x^2+ 14x + 48 This is basically a quadratic equation, so here we will us middle term splitting method, which is shown below That is: - x^2 + 6x + 8x + 48 Therefore x(x+6) + 8(x+6) = 0 So (x+8) (x+6) = 0 From above equation we have seen that x = -8 and x = -6 is the required solution of the given equation. Question 2:- Factor the following expression: - x^3+ 11 x^2 +11 x+ 121 Solution 2:- In this question given expression is x^3 + 11x^2 + 11 x + 121 There is basically no common factor in above equation for all four terms. But it is quite clear that there is some common factor between first and second term and also between third and fourth term. So we will take common accordingly Therefore x^3 + 11 x^2 + 11 x + 121 = x^2 (x+ 11) + 11 (x+11) Now we can see that (x+11) can be taken out So x^3 + 25x^2 + 25x + 625= (x+11) (x^2 +11)

The Best Websites to Learn Chinese

The Best Websites to Learn Chinese The Best Online Resources for Learning Mandarin Chinese Chapters Forvo Chinese Forums Jukuu Memrise FluentU Coursera Global ExamSuperprofLearning to read and write in Chinese used to be just for those taking the subject at university. However, thanks to the boom in the Chinese economy and the Confucius Institute, if you want to take Mandarin lessons, there are Chinese classes all over the world.In fact, there are plenty of universities that offer degrees in Chinese, Chinese evening classes at community centres and language schools, and private tutors up and down the country who are ready to teach you all about the Chinese language.In addition to all the classes and tutorials popping up, the Chinese language has seen a digital boom, too! The Chinese language is now everywhere and, as a result, there are plenty of ways to learn the language with just the click of a mouse.In the early days of the world wide web, there were only a few sites that held a monopoly on learning Chinese online and if you wanted to speak Chinese, you had a very limi ted choice.  Nowadays, on the other hand, there are now so many sites that it can be difficult to work out which methods work the best and which sites you should be using to help you learn Mandarin Chinese!That’s where the Superprof team comes in to save the day with the best websites for learning Chinese! Whether you're struggling with Chinese characters, looking for Chinese lessons, wanting to move to Beijing, or just interested in learning more about Chinese culture, these are the websites you need to visit. NingChinese Teacher 5.00 (10) £25/h1st lesson free!Discover all our tutors LorraineChinese Teacher £10/h1st lesson free!Discover all our tutors YuweiChinese Teacher 4.33 (6) £19/h1st lesson free!Discover all our tutors JoyceChinese Teacher £15/h1st lesson free!Discover all our tutors NicoleChinese Teacher £60/h1st lesson free!Discover all our tutors KatyChinese Teacher £16/h1st lesson free!Discover all our tutors YangChinese Teacher £18/h1st lesson free!Discover al l our tutors ChengChinese Teacher £20/h1st lesson free!Discover all our tutors ForvoLearning foreign languages on the Internet has never been simpler! You'll have probably noticed that learning Standard Mandarin Chinese on the Internet is becoming increasingly popular, too, and, as a result, it's never been easier to learn Chinese online.Which learning method should you use when you first start learning Chinese? (Source: rawpixel.com)If you're learning a language on your own or online, pronunciation might be something you'll struggle with since there's nobody around to correct you. This is where a site like Forvo comes in really handy!While this site isn't geared towards teaching you grammar, vocabulary, phrases, or even tones in the traditional sense, every Chinese learner should add “Forvo” to their browser favourites. Forvo is a fantastic resource for mastering Chinese pronunciation.  Just type whatever Chinese word you’d like to pronounce into the search bar and the websi te will tell you exactly how it’s pronounced.However, this isn’t just a website for those learning Chinese. Forvo claims to have pronunciations for every word in the world!  While this probably isn’t true, there are still tonnes of different languages available with multiple examples of pronunciations for each word from Chinese people. In addition to words, there are also examples of full sentences, expressions, and idioms for you to listen to as well.If you prefer to learn Chinese on the go, you should check out our apps for learning Chinese, too! Chinese ForumsIf you want to improve you Chinese from the comfort of your own home, you need to get involved with communities of other language learners, too.Are digital resources the way forward when it comes to learning Chinese? (Source: pixabay.com)Chinese Forums is one of the best places to go if you have any questions about learning Chinese or are having a problem.  There are plenty of very active users who are happy to help ab solute beginners as well as more experienced students.  You can find the answers to almost all of your questions on Chinese here as well as meet other forum users who are just as interested in Chinese as you.The best thing, though? It’s completely free! JukuuWhile dictionaries are great for looking up words, you’ll understand a word much better if you can see it being used in context or in a sentence.Are classrooms like this a thing of the past? (Source: pixabay.com)This is where Jukuu comes into play. Jukuu is more than a dictionary, it’s a search engine for Chinese-English sentences and translations so that you can see both what the word means and how you’d use it in a sentence.Personally, I find that these kinds of websites are far more useful than dictionaries since an out-of-context translation of a word can result in you completely misunderstanding a word or a whole sentence.Discover more books that you can learn Chinese from... NingChinese Teacher 5.00 (10) £25/h1st lesson free!Discover all our tutors LorraineChinese Teacher £10/h1st lesson free!Discover all our tutors YuweiChinese Teacher 4.33 (6) £19/h1st lesson free!Discover all our tutors JoyceChinese Teacher £15/h1st lesson free!Discover all our tutors NicoleChinese Teacher £60/h1st lesson free!Discover all our tutors KatyChinese Teacher £16/h1st lesson free!Discover all our tutors YangChinese Teacher £18/h1st lesson free!Discover all our tutors ChengChinese Teacher £20/h1st lesson free!Discover all our tutors MemriseMemrise is a website that includes plenty of different courses. There are plenty of different e-learning tools on their website  for a variety of different languages including Chinese!While Memrise is free, it also includes a “Pro” version that includes things like: Learn and review, grammarbot, pro chats, difficult words mode, speed Review, listening skills mode, video mode, and learning stats. The free mode, on the other hand, only includes the learn and review function. FluentUFluentU is a platform that offers Chinese language classes through videos and includes a plethora of video resources for a variety of different languages.  While it’s not free, there are “basic” and “plus” subscription packages which you can cancel at any time. The “plus” subscription for $20 a month includes:iPhone, iPad AppUnlimited Word LookupUnlimited Videos, AudiosUnlimited FlashcardsUnlimited QuizSpaced RepetitionCreate Your Own FlashcardsFluentU works by taking entertaining videos in the target language, transcribing them, subtitling them, and then translating them. All you have to do is watch them and pay attention!Is learning online enough to start speaking Chinese when you land? (Source: kaboompics.com)This means you can enjoy real Chinese videos from Chinese-speaking countries rather than materials that have been specifically for language learning.  This method works by enabling you to create your own immersion environment where you can expe rience Chinese-language culture for less than the cost of a plane ticket.  There are also quizzes so that you can test yourself and see how you’re progressing.Finally, there’s also an app available so that you can benefit from your FluentU subscription whilst you’re on the go or waiting for a bus, etc.Also discover how may videos you could learn Chinese from! CourseraThe Coursera platform is a Massive Open Online Course (commonly known as a MOOC) which was founded by professors from the Stanford University.  The platform includes over 2,000 courses and currently has over 28 million registered users. Of course, Chinese language courses make up some of the courses available on the platform.There are literally tonnes of different courses for those wanting to learn Chinese from beginners, intermediate, and advanced classes to HSK preparation courses and a  large number of these courses are run by universities in China, too! Global ExamGlobal Exam is a platform that offers training for language proficiency tests including the DELE (Spanish), DELF (French), WiDaF (German), and, most importantly, the HSK for Chinese. The platform includes 120 HSK training sessions of which 24 are HSK training exams. This gives you 180 hours of practice and nearly 9,000 questions.You can also use the scheduling feature to plan your training and revision sessions in order to make effective use of your time.  As you get closer to the day, you can also make use of the exam mode and take practice HSK exams under exam conditions.You’ll also get detailed corrections so that you know where you’re going wrong and links to where you can study the things you got wrong.  Don't forget to keep track of your progress with the detailed statistics and see how effectively you’ve been using your time, too.You’ll hardly be surprised to find out that this service isn’t free. However, if you get an annual subscription, you’ll end up paying just over £150.SuperprofWe could hardly have wr itten an article on online Chinese resources and not mention ourselves, could we? Aside from immersion (which is by and far the best way to learn Chinese how to speak a new language), the best way to learn Chinese is with a Chinese teacher or tutor.While there are plenty of exceptional online Chinese courses (as we've mentioned above) and free Chinese resources, they all lack one thing: a personalised approach.When you study Chinese (just like any other language), you will inevitably hit a few speed bumps on your road to fluency. This is where a private tutor can help.Since a private tutor teaches you and only you, their lessons are geared towards your strengths and weaknesses and your own personal goals. For example, if you're just starting out, they can use the Chinese Pinyin transcription system to help you learn new vocabulary. If you're looking to move to Mainland China, they can focus on conversational classes and get you speaking Chinese as soon as possible. Whether you're lo oking for Mandarin lessons London, tutors for Chinese in London, or Cardiff or anywhere else for that matter, you can find them with us.Of course, while private tutorials aren't as cheap as some of the other methods you can use to learn to speak Chinese, they are significantly cheaper than a flight to China and are definitely the option you should be taking if you've already bought your flights and need to get to grips with the language before you go.If you're looking for a textbook to complement your Chinese course, you should check out our list of best tools for learning Chinese!

Understanding Some Common Errors In English To Avoid Them

Understanding Some Common Errors In English To Avoid Them English is a subtle language with many tricky grammatical patterns. Even a well versed person in English tends to err in English grammar and more so in the case of a common practitioner of the language. English grammar is tricky with rules and exceptions to rules. Writing English with flawless grammar is a matter of practice and it needs extended knowledge in the grammatical patterns of the language. Following are some common grammatical errors caused by misunderstandings and insufficient knowledge in English grammar Confusion in placing apostrophes Confusion in placing apostrophes is a very common error. For example, The word ‘It‘ is a pronoun and its without apostrophe means its possession. Examples are A) The bird is beautiful. Its feathers are multi colored. B) It’s perching on the branch of a tree. In the first sentence, the phrase ‘its feathers’ denotes the feathers of the bird and thus the word ‘its’ (without apostrophe) denotes possession. In the second sentence, the word ‘it’s’ (with apostrophe) is the contraction of the words ‘it is’. It denotes the action of the bird (perching). Access Online #English Tutor For Mastery Of 4 #Language #Skills http://t.co/jJ1rfCHwCI pic.twitter.com/ZWHZSDJFu3 â€" Tutor Pace (@TutorPace) July 27, 2015 It is important to know where to use apostrophes. Same confusion can be felt in the next example as well. C) There are 20 students in the class. D) Many students’ books were lost. E) A student’s money was also lost. In the first sentence, the word ‘students ‘denotes the number (how many) of the students. So, it is just a plural noun where there is no need for any apostrophe. In the second sentence, ‘students’ points out the meaning- books belong to students (possession). So, there is a need for using apostrophe in ‘students’. Third sentence contains a singular noun ‘student’ where apostrophe falls in between the letters ‘t’ and s’ to specify the singularity of the noun. If we misuse the apostrophe, the sentence loses its sense. Confusing pronouns Pronouns are the words used in the place of nouns. Confusing first person pronouns is a very common error found in English language usage. For example, ‘He and I went for a party yesterday’ is the correct sentence and if one uses He and me went for a party yesterday’, it is wrong. Same way, you should not use ‘He talked to I’. Instead you should say ‘He talked to me’. It is because the letter I is the subject pronoun and ‘me is the object pronoun and they cannot be misplaced. Same way, ‘myself’ is the reflexive pronoun which should be used only for repetition as in ‘I patted myself for the good job done’. Mixing homophones Homophones are words that have similar sound patterns but are different in meaning and in most cases carry different spellings. If one changes the homophones, the entire meaning changes or there is no sense at all. When you write ‘bow’ in the place of ‘bough’, the entire meaning is lost as in the sentence ‘The hunter took the arrow and bough to hunt the deer’- bough and bow sound the same but they differ in spelling and meaning. Bough is the branch of a tree and the other bow goes with the arrow. Similarly then denotes time and than is a comparative word. The pairs like there and their also are homophones often confused. Confusing words of quantity Countable and uncountable words are often confused by people. Examples are ‘A number of people attended the meeting yesterday’- The word ‘number’ is used, as the noun ‘people’ is countable. ‘He withdrew a large amount of money from the bank’-the word ‘amount’ is used with ‘money’, since it is uncountable. Agreement of the verb with the subject Using plural verbs in the place of singular ones is a common error. Take the word ‘mathematics’ or ‘news’. Though they end in the letter ’s’, they are not plural in meaning. So, one should write ‘The news is false’ and ‘Mathematics is an interesting subject’. Same way, collective nouns do not take plural verbs as in 1000 million dollars is a big sum. Why You Need To Focus On Your #English #Skills For Success In Your #career And Life http://t.co/4z4qVBMUNR pic.twitter.com/B6gSw2goLe â€" Tutor Pace (@TutorPace) July 28, 2015 Many more errors in English usage are there. If students find them hard to fix, they can take recourse to an online English tutor who sets them right for him through customized solutions. Online English tutoring is the best bet for students who struggle in English grammar.

2018 Official Guide to the GMAT Review Series Problem #23 (Algebra Distance-Rate Problems)

2018 Official Guide to the GMAT Review Series Problem #23 (Algebra Distance-Rate Problems) GMAT MBA Admissions Blog This post is the fourth in our series on using strategies to answer specific questions from the 2018 Official Guide. Here, one of our most experienced GMAT tutors, John Easter, analyzes a question about distance-rate. During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During the time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel? (A) 36 (B) 37.5 (C) 40 (D) 80 (E) 90 This is a basic distance-rate problem, but the standard D = RT table isn't very convenient here. Before I jump in, I'm going to do some estimation/approximation and see if I can eliminate some of the answer choices. First, 1 mile per minute = 60 miles per hour. Second if 5 gallons is equivalent to 2 hours of travel, 3.75 gallons will be more than one hour (it's more than half of 5 gallons). So, Car X has obviously gone more than 60 miles. A, B, and C are out. Now if I round 3.75 gallons to 4 gallons, then the corresponding travel time will be 4/5 of 2 hours = 4/5(2) = 8/5 hours. At 60 miles per hour, that's 60(8/5) = 96 miles Because I rounded up, this should be slightly larger than the exact distance. The correct answer is E. If that's a little bit too seat-of-the-pants for you, we can use a proportion and solve for the exact amount of travel time: 3.75/5 = x/2 (2)(3.75) = 5x And x equals 7.5/5 = 15/10 = 3/2. So 1.5 hours at 60 miles per hour is exactly 90 miles. About the Author John Easter is one of MyGuru’s longest tenured and most experiencedGMAT tutors. He is also the founder ofOwl Test Prep, another great source for GMAT advice.