Question

Barbara walked up and down a 25 meter long corridor. When she walked one way, she walked at 4 meters per second, and when she walked the other way, her speed was 2 meters per second. If barbara completed walking up and down that corridor 5 times, what was her average speed in meters per second?

Answer 1

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We can use the average rate formula:

average rate = total distance/total time

average = 50/(25/4 + 25/2)

average = 50/(25/4 + 50/4)

average = 50/(75/4)

average = 200/75 = 8/3 = 2 2/3

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Answer 2

If you know weighted average principles, you can answer the question almost immediately. Walking the same distance will take you twice as long if you walk half as fast. So Barbara spends twice as long walking at 2 m/s as she does at 4 m/sec. Her average speed must be between 2 and 4, but because she spends twice as long walking at 2 m/s, her average speed will be 'twice as close' to 2, so must be D.

That explanation will only make sense to someone who has learned weighted averages properly. We can do algebra instead. Her times will be 25/2 and 25/4 seconds for the two parts of the trip, so her total time is 75/4 seconds, and her total distance is 50 meters. We find average speed by dividing total distance by total time:

50 / (75/4) = 50*4/75 = 2*4/3 = 8/3

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