Distance, rate & time drills

Solve problems using distance = rate x time.

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

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How to solve distance, rate and time problems

Every problem uses one formula: distance = rate × time. Rearrange it for what you need:

Units must match. If the speed is in miles per hour, the time must be in hours. Change minutes to hours by dividing by 60: 150 minutes is \(150 \div 60 = 2.5\) hours, so 100 miles in 150 minutes is \(100 \div 2.5 = 40\) mph.

For a trip with two parts, find the distance of each part, then add them.

Traps:

Worked examples

Example 1.
A cargo ship sails at 22 mph for 3 hours, then at 12 mph for 120 minutes. What is the total distance traveled, in miles?
Show answer and explanation
Answer:
B

Leg 1: 22 \(\times\) 3 = 66 mi. Leg 2: convert 120 min \(= 120 \div 60 = 2\) h, so 12 \(\times\) 2 = 24 mi. Total \(= 66 + 24 = 90\) mi. (Forgetting the second leg gives 66 miles. Averaging the two speeds and multiplying by the total time gives 85 miles. Forgetting the first leg gives 24 miles.)

Example 2.
A delivery truck drives 72 miles at a constant speed of 48 mph. How long does the trip take?
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Answer:
D

Time \(=\) distance \(\div\) speed \(= 72 \div 48 = 1.5\) hours, which is 1 hour 30 minutes. (Writing \(72 \div 48 = 1\) R \(24\) as 1 hour 24 minutes gives 1 hour 24 minutes. Reading the 0.5 in 1.5 hours as 50 minutes gives 1 hour 50 minutes. Changing 1.5 hours to minutes with 100 minutes in an hour (\(150\) minutes) gives 2 hours 30 minutes.)

Example 3.
A city bus travels 40 miles in 150 minutes at a constant speed. What is the city bus's speed, in miles per hour?
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Answer:
D

Convert minutes to hours: 150 min \(= 150 \div 60 = 2.5\) h. Speed \(=\) distance \(\div\) time \(= 40 \div 2.5 = 16\) mph. (Writing 150 minutes as 1.5 hours (\(40 \div 1.5\)) gives about 26.7 mph. Writing 2 h 30 min as 2.30 hours (\(40 \div 2.30\)) gives about 17.4 mph. Dividing by the 2 whole hours only (\(40 \div 2\)) gives 20 mph.)