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Difficulty: EasyRate, Time, and Distance Problems

A delivery van travels from Warehouse A to Warehouse B at a constant speed of 4040 miles per hour and returns along the exact same route from Warehouse B to Warehouse A at a constant speed of 6060 miles per hour. If the distance between Warehouse A and Warehouse B is 120120 miles, what is the average speed of the delivery van for the entire round trip, in miles per hour?

Answer: 48 miles per hour

Answer

The average speed for the entire round trip is 4848 miles per hour.
To find the average speed for the round trip, divide the total distance (240240 miles) by the total time taken (55 hours). The time taken for the first leg is 12040=3\frac{120}{40} = 3 hours, and for the return leg is 12060=2\frac{120}{60} = 2 hours. Thus, the average speed is 2405=48\frac{240}{5} = 48 miles per hour.

Step-by-Step Solution

1
Determine the total distance traveled during the round trip.
The distance from Warehouse A to B is 120120 miles, making the total round-trip distance 120+120=240120 + 120 = 240 miles.
Average speed requires the total distance for all legs of the journey.
2
Calculate time taken for each leg and find total time.
Time taken at 4040 mph is 12040=3\frac{120}{40} = 3 hours. Time taken at 6060 mph is 12060=2\frac{120}{60} = 2 hours. Total time = 3+2=53 + 2 = 5 hours.
Time equals distance divided by rate (t=drt = \frac{d}{r}).
3
Divide total distance by total time to obtain average speed.
Average speed = 240 miles5 hours=48\frac{240 \text{ miles}}{5 \text{ hours}} = 48 miles per hour.
The defining formula for average speed is Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}.

Key Concept

Average speed for a multi-leg journey is always total distance divided by total time, not the arithmetic mean of the speeds.
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Topics

Rate, Time, and Distance Problems

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