# IIM-CAT: How to Calculate Speed, Time & Distance

Word problems on Test Day that ask about speed, time, and distance often appear on the IIM-CAT Problem Solving test. Let’s review two important equations to remember for better scores and look at two sample IIM-CAT practice questions involving speed, time & distance.

The first important formula to memorize is: **D = R x T**. This stands for Distance = Rate x Time. I like to think of it as the “DIRT” formula and writing it this way is the easiest way for me to remember. It is perfectly acceptable to also think of it as Time = Distance / Rate or as Rate = Distance / Time.

The second formula is: **Average Rate = Total Distance / Total Time**. You will notice that it is NOT the mean, or the mathematical average of the speeds, so don’t let the word “average” confuse you. Average Rate is completely different. Let’s look at an example question:

Give this IIM-CAT speed, time, and distance Grockit question a shot!

*I got in my car and drove 40 miles to see my cousin and was going 20 mph. It took me 2 hours to get there. Then, I left my cousin’s and drove another 30 miles to the store but this time went 10mph. It took me 3 hours to arrive at the store. What was my “Average Speed” for the whole trip? *

Average Speed = Total Distance / Total Time. I traveled 40 miles + 30 miles so my Total Distance was 70 miles. I drove for 2 hours + 3 hours so my Total Time was 5 hours. 70/5 = 14. My Average Speed for the whole trip was 14 mph. Think of Average Speed as a weighted average. I spent more time going 10mph than 20mph, so it makes sense that the Average Speed would be closer to 10mph.

*Tracey ran to the top of a steep hill at an average pace of 6 miles per hour. She took the exact same trail back down. To her relief, the descent was much faster; her average speed rose to 14 miles per hour. If the entire run took Tracey exactly one hour to complete and she did not make any stops, how many miles is the trail one way? *

For the way up the hill, we know that D = 6mph x T. For the way down the hill, we know that D = 14mph x T. Since we went know that the distance up the hill was the same as the distance down the hill, we can pick a number for D. Let’s choose “84” since it is a multiple of both 6 and 14. If 84 = 6mph x T, then we know that T = 14 hours. If 84 = 14mph x T, then we know that T = 6 hours. Now we can use another formula, the Average Rate formula, to find the average speed for the WHOLE trip. Average Rate = Total Distance / Total Time

Using our Picked Number of 84, we know that the Total Distance traveled would be 168 miles. The Total Time is 14 hours + 6 hours = 20 hours. So the Average Rate = 168 miles / 20 hours = 8.4 mph. It doesn’t matter that Tracey didn’t “really” go 168 miles, or that we know she didn’t “really” go 20 hours. We Picked a Number just so that we could find the ratio of the Total Distance to the Total Time in order to calculate the Average Rate of the ENTIRE journey.

Now that we have found the Average Rate for the whole trip, we can plug it in to the “DIRT” formula to find the ACTUAL distance for the entire journey. We know that T = 1 hour because the problem told us so. Therefore, the actual distance for the entire trip was 8.4 miles. The problem asks how many miles the trail was one way. 8.4 / 2 = 4.2. The answer to the question is 4.2 miles.

To get more practice with Grockit’s “Speed, Time & Distance” questions, click on the Practice section in the IIM-CAT Lobby and then click on “Create Game.” Select “Customize Difficulty” and click on the “Speed, Time & Distance” skill tag. You might also like to select the “Word Problems” tag since you’ll find these two skills frequently overlap! Happy Grockiting!

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