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Question

Difficulty: MediumRound Trips

A cyclist travels from her home to a nearby town, a distance of 1515 miles, at an average speed of 1212 mph. On the return trip along the same route, her average speed is 2020 mph. What is her average speed, in mph, for the entire round trip?

Answer: 15 mph

Answer

15
The correct average speed is found by dividing the total round-trip distance (3030 miles) by the total travel time (22 hours), resulting in 1515 mph.

Step-by-Step Solution

1
Calculate the time for the outbound trip.
1.25 hours
Time equals distance divided by speed (15 miles/12 mph=1.25 hours15 \text{ miles} / 12 \text{ mph} = 1.25 \text{ hours}).
2
Calculate the time for the return trip.
0.75 hours
Time equals distance divided by speed (15 miles/20 mph=0.75 hours15 \text{ miles} / 20 \text{ mph} = 0.75 \text{ hours}).
3
Determine the total time and total distance for the entire round trip.
Total time = 2 hours, Total distance = 30 miles
Adding the outbound and return times (1.25+0.751.25 + 0.75) gives 2 hours. The round trip is twice the one-way distance (15×215 \times 2).
4
Calculate the average speed for the entire round trip.
15 mph
Average speed is total distance divided by total time (30 miles/2 hours=15 mph30 \text{ miles} / 2 \text{ hours} = 15 \text{ mph}).

Key Concept

Average Speed for a Round Trip
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Topics

Round Trips

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