Average rate drills

Find average speed or rate over multiple legs of a trip.

Free, timed SHSAT practice sets on average rate— every question includes a full worked explanation, and there's no account required.

Loading questions…

How to solve average speed problems

Average speed is total distance divided by total time. It is usually not the average of the speeds.

  1. Add all the distances.
  2. Add all the times in the same unit. Change minutes to hours by dividing by 60.
  3. Divide total distance by total time.

Example: you drive 90 miles at 30 mph (3 hours), then 90 miles at 90 mph (1 hour). Average speed \(= \dfrac{180}{4} = 45\) mph, not 60 mph. You spend more time at the slower speed, so the average is pulled toward 30.

Traps:

Worked examples

Example 1.
A delivery truck drives 27 miles in 1.5 hours, then 133 miles in 150 minutes. What is the delivery truck's average speed for the entire trip, in miles per hour?
Show answer and explanation
Answer:
C

Average speed \(=\) total distance \(\div\) total time, NOT the average of the leg speeds. Total distance \(= 27 + 133 = 160\) mi. Total time \(= 1.5 + 150 \div 60 = 4\) h. Average speed \(= 160 \div 4 = 40\) mph. (Averaging the two leg speeds gives 35.6 mph. Writing 150 minutes as 1.5 hours (\(160 \div (1.5 + 1.5)\)) gives about 53.3 mph. Using the first leg's speed only (\(27 \div 1.5\)) gives 18 mph.)

Example 2.
On a trip, a city bus covers 37 miles in 2.5 hours, then 9 miles in 0.5 hours, then 86 miles in 3 hours. What is the average speed for the whole trip, in miles per hour?
Show answer and explanation
Answer:
C

Total distance \(= 37 + 9 + 86 = 132\) mi. Total time \(= 2.5 + 0.5 + 3 = 6\) h. Average speed \(= 132 \div 6 = 22\) mph. (Averaging the three leg speeds gives about 20.5 mph. Dropping the third leg (\(46 \div 3\)) gives about 15.3 mph. Dividing the total distance by 3, the number of legs (\(132 \div 3\)) gives 44 mph.)