Distance, Speed & Time
Solving problems using d = r Γ t, average speed, and multi-leg journey calculations
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Have you ever raced your best friend to grab the very last slice of pepperoni pizza? π If you both start from the same spot, the person who runs the fastest (speed) for the shortest amount of time will cover the distance first and win the pizza! Welcome to the world of Distance, Speed, and Time. This is one of the most useful math tricks you will ever learn, and the SSAT test makers absolutely love it. Why? Because we use it every single day!
Whether you are figuring out how long a boring car ride will take, or tracking how fast a cheetah can run, it all comes down to one simple idea. Distance is how far you go. Speed (or rate) is how fast you are moving. Time is how long it takes. To solve these puzzles on the SSAT, you just need to remember the magic formula: (Distance equals Rate times Time). ππ¨
I like to picture a giant triangle with a 'D' at the top, and 'R' and 'T' at the bottom. If you want to find Distance, you multiply Rate and Time. If you want to find Time, you divide Distance by Rate (). And if you want to find Rate, you divide Distance by Time (). Once you master this magic trick, you will be zooming through these SSAT math questions faster than a superhero flying to the rescue! π¦ΈββοΈ Let's look at some super fun examples to get you ready.
Practice Questions
3 practice questions for SSAT Middle Level
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- Average speed is calculated as total distance divided by total time. First, find the total distance: 30 miles + 20 miles = 50 miles. Next, find the total time: 90 minutes + 1 hour. Since 1 hour = 60 minutes, the total time is 90 + 60 = 150 minutes. Convert the total time into hours: hours. Finally, divide the total distance by the total time in hours: miles per hour.
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- Average speed = total distance / total time. The total distance for the round trip is 120 miles + 120 miles = 240 miles. The time for the trip to the warehouse is hours. The time for the return trip is hours. The total time for the round trip is 2 + 3 = 5 hours. To find the average speed, divide the total distance by the total time: miles per hour.
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- To find the average speed, use the formula: Average speed = total distance / total time. The total distance is 40 miles + 50 miles = 90 miles. The total time is 1 hour (which is 60 minutes) + 90 minutes = 150 minutes. Convert 150 minutes into hours: hours. Divide the total distance by the total time: miles per hour.
Tips & Strategies
- Draw the D-R-T magic triangle on your scratch paper! Put a 'D' on top, and an 'R' and 'T' on the bottom. Cover up the letter you are looking for, and the triangle tells you exactly what math to do.
- Always check your units! If the speed is in miles per hour, but the time given is in minutes, you MUST convert the minutes into hours (like changing 30 minutes into hour) before multiplying.
- For Average Speed questions, write down 'Total Distance' and 'Total Time' before doing anything else. Never just add two speeds together and divide by 2!
Common Mistakes
- Watch out for mixed-up units! If a question asks how far a train travels in 15 minutes at 60 miles per hour, don't multiply 60 by 15! You must change 15 minutes into hour first.
- Don't forget the golden rule of average speed: it is ALWAYS . The SSAT loves to put the wrong 'simple average' as an answer choice to trick you.
Frequently Asked Questions
Will the SSAT give me the distance formula on the test?
Nope! You have to memorize it. Just remember the word 'Dirt' () to help it stick in your brain!
What if the distance is in kilometers instead of miles?
Don't panic! The math works exactly the same way. Just make sure your speed matches, like kilometers per hour!
Are there really average speed questions on the SSAT?
Yes, especially on the Middle and Upper Level tests. They love to trick students who just try to find the middle of two speeds, so always use your total distance and total time.
Can I use a calculator for the tricky fractions?
Calculators are not allowed on the SSAT. That's why practicing multiplying and dividing fractions, like or , is super important!