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Question

Difficulty: EasyRate, Time, and Distance Problems

A cyclist travels from Town A to Town B, a distance of 6060 miles, at a constant speed of 3030 miles per hour. On the return trip from Town B to Town A along the exact same route, she travels at a constant speed of 2020 miles per hour. What is the cyclist's average speed, in miles per hour, for the entire round trip?

  1. A
    25 miles per hour
  2. 24 miles per hourAnswer
  3. C
    50 miles per hour
  4. D
    12 miles per hour
  5. E
    10 miles per hour

Answer

24 miles per hour
To find the average speed for any multi-leg trip, divide total distance by total time. The first leg of 6060 miles at 3030 mph takes 22 hours. The return leg of 6060 miles at 2020 mph takes 33 hours. The total distance is 120120 miles and total time is 55 hours. Therefore, the average speed is 1205=24\frac{120}{5} = 24 miles per hour.

Step-by-Step Solution

1
Calculate the time taken for the trip from Town A to Town B.
t1=6030=2t_1 = \frac{60}{30} = 2 hours
Time equals distance divided by speed.
2
Calculate the time taken for the return trip from Town B to Town A.
t2=6020=3t_2 = \frac{60}{20} = 3 hours
Time equals distance divided by speed.
3
Find the total distance and total time for the round trip.
Total Distance = 60+60=12060 + 60 = 120 miles; Total Time = 2+3=52 + 3 = 5 hours
Average speed is based on the entire journey's distance and duration.
4
Compute the average speed.
\text{Average Speed} = \frac{120}{5} = 24\text{ miles per hour}
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}

Key Concept

Average Speed for a Multi-Leg Trip
Estimated Time:1m 0s
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Topics

Rate, Time, and Distance Problems

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