Distance, Speed & Time
Solving problems using d = r × t, average speed, and multi-leg journey calculations
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Have you ever wondered how long it would take a cheetah riding a skateboard to travel to your favorite pizza place? 🐆🍕 That's exactly what distance, speed, and time problems are all about! On the ISEE, you will act like a math detective figuring out how far someone traveled, how fast they were going, or how much time their epic journey took.
To solve these mysteries, we use a super famous math rule: Distance equals Rate times Time. Think of "Rate" as just a fancy test-word for "Speed." If you ride your bike at a speed of 10 miles per hour for 2 hours, you just multiply them together to find out you traveled 20 miles! Easy peasy, right? 🚲💨
The ISEE Quantitative Reasoning and Mathematics Achievement sections love to test this. Sometimes they will give you the distance and the time, and ask you to find the speed. Other times, they might ask about a tricky multi-leg journey, like walking to the park and then running back home. Just remember to keep your units (like miles and hours) matching, and you'll be zooming through these questions in no time! Plus, there is no penalty for guessing on the ISEE, so if you ever get stuck on a speed bump, just pick your favorite letter and keep on rolling!
Practice Questions
3 practice questions for ISEE Middle Level
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- To find the time for each trip, use the formula . For Column A, the time it takes Train A is hours. For Column B, the time it takes Train B is hours. Since is greater than , the quantity in Column A is greater.
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- First, convert the time from minutes to hours so the units match the speed. Since there are 60 minutes in an hour, 45 minutes is equal to of an hour, which simplifies to of an hour. Using the formula , multiply the speed ( miles per hour) by the time ( hour): . The bicyclist travels 9 miles.
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- To find the total time, calculate the time spent on each half of the trip separately using . For the first 30 miles, her time is hour (or 30 minutes). For the second 30 miles, her time is hour. Add the two times together: hours.
Tips & Strategies
- Draw a 'DIRT' triangle to remember the formulas! Write 'D' at the top of a triangle, and 'R' and 'T' at the bottom. To find one, cover it up! Cover D, and you see R next to T (). Cover T, and you see D over R ().
- Watch your units! If your speed is in miles per hour but your time is in minutes, you must convert the minutes into a fraction of an hour (like 30 minutes = hour) before doing any math.
- For Quantitative Comparison questions, check if you even need to do the math. If Column A has a longer distance but a much faster speed than Column B, you might be able to estimate the answer without doing long division.
Common Mistakes
- Watch out for 'Average Speed' tricks! You CANNOT just add two speeds together and divide by 2. To find average speed for a whole trip, you must use .
- Don't forget to check that your units match. Multiplying miles per hour by minutes without converting will give you a wacky, wrong answer that the test makers might put as a trap answer choice!
Frequently Asked Questions
What does the word 'Rate' mean on the ISEE?
Rate is just a fancy test-word for 'speed'. If a question asks for the rate of a car, it just wants to know how fast the car is going in miles per hour or feet per second!
What if a trip has two different parts?
Break it into chunks! Create a mini D-R-T chart for Part 1 of the trip, and another chart for Part 2. Solve them separately before adding the distances or times together.
Is there a penalty if I guess on a really hard speed question?
Nope! The ISEE does not have a guessing penalty. If a multi-leg journey question is taking up too much time, take your best guess, bubble it in, and move on to an easier question.
Why do we use fractions for time and rate?
Because division is the same thing as a fraction! Writing is just a cleaner way for mathematicians to write '10 divided by 2'. It makes simplifying the math much easier.