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KCC's quiz AQQ274 about 2 sportsmen running and walking

Two  sportsmen A and B have exactly the same running speed and the same walking speed.

One day they started the same trip to the same place.

Sportsman-A walked for half of the distance and ran for the rest, while

Sportsman-B walked for half the time and ran for the other half of time.

Question: Which sportsman reached the end of the trip first? How do you justify it?

Good luck and try to be among the firsts!

P.S. Pass those quizzes among your colleagues and friends; we all need such small brainstorming time to time!

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  • B finishes first.

    A walks half distance and runs half distance

    B walks half of the TIME and runs half of the TIME

    We can assume that running is faster than walking

    Total time for A is proportional to 0.5/W +0.5/R, where W and R are the speed of walking and running.

    B walks half of the TIME and runs half of the TIME

    Given the assumption that running is faster than walking, we can see that B will run for more than half the distance, since the running TIME is the same as the walking TIME

    Since B is running for more than half the distance and running is faster than walking, B will finish the trip first, since A will run only half the distance and therefore for less time.

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  • B finishes first.

    A walks half distance and runs half distance

    B walks half of the TIME and runs half of the TIME

    We can assume that running is faster than walking

    Total time for A is proportional to 0.5/W +0.5/R, where W and R are the speed of walking and running.

    B walks half of the TIME and runs half of the TIME

    Given the assumption that running is faster than walking, we can see that B will run for more than half the distance, since the running TIME is the same as the walking TIME

    Since B is running for more than half the distance and running is faster than walking, B will finish the trip first, since A will run only half the distance and therefore for less time.

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