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Question

Difficulty: MediumRate, Time, and Distance Problems

An executive drives from Office A to Office B, a distance of 120120 miles, at a constant speed of 4040 miles per hour. After spending exactly 11 hour at Office B for a meeting, she returns to Office A along the exact same route at a constant speed of 6060 miles per hour. What is her average speed, in miles per hour, for the entire round trip including the time spent at Office B?

  1. A
    3535
  2. 4040Answer
  3. C
    4545
  4. D
    4848
  5. E
    5050

Answer

The average speed for the entire round trip, including the meeting time, is 4040 miles per hour.
To find the average speed for the entire trip, divide total distance covered by total time elapsed. The total distance is 120+120=240120 + 120 = 240 miles. The travel time outbound is 120/40=3120 / 40 = 3 hours, and the travel time return is 120/60=2120 / 60 = 2 hours. Including the 11-hour meeting at Office B, the total elapsed time is 3+1+2=63 + 1 + 2 = 6 hours. Thus, the overall average speed is 240/6=40240 / 6 = 40 miles per hour.

Step-by-Step Solution

1
Calculate the travel time for the outbound leg from Office A to Office B.
Timeoutbound=120 miles40 mph=3 hours\text{Time}_{\text{outbound}} = \frac{120\text{ miles}}{40\text{ mph}} = 3\text{ hours}.
Time equals distance divided by speed.
2
Calculate the travel time for the return leg from Office B to Office A.
Timereturn=120 miles60 mph=2 hours\text{Time}_{\text{return}} = \frac{120\text{ miles}}{60\text{ mph}} = 2\text{ hours}.
Time equals distance divided by speed.
3
Determine the total distance and total elapsed time for the entire trip.
Total Distance=120+120=240 miles\text{Total Distance} = 120 + 120 = 240\text{ miles}; Total Time=3 hours (outbound)+1 hour (meeting)+2 hours (return)=6 hours\text{Total Time} = 3\text{ hours (outbound)} + 1\text{ hour (meeting)} + 2\text{ hours (return)} = 6\text{ hours}.
Average speed requires total distance divided by total time elapsed, which must include non-moving meeting time.
4
Calculate the overall average speed.
Average Speed=240 miles6 hours=40 miles per hour\text{Average Speed} = \frac{240\text{ miles}}{6\text{ hours}} = 40\text{ miles per hour}.
Divide total distance by total time.

Key Concept

Average Speed for Multi-Leg Journeys
Estimated Time:2m 0s
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Topics

Rate, Time, and Distance Problems

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