Number Problem 21

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From A, a young man takes 20 minutes to reach his work spot whereas an old man takes 30 minutes.
When will the young man catch up the old man if the latter starts 5 minutes before him?

Solution: The speed of the young man : The speed of the old man = 1/20 : 1/30 = 3 : 2

Let the speed of the young man be 3x meters per minute and that of the old man be 2x meters per minute.

If the young man takes y minutes to catch up the old man, then the distance traversed by him = 3xy meters.

The distance traversed by the old man = 2x (y + 5) meters

3xy = 2x (y + 5)

3y = 2(y + 5)

y = 10

The young man will catch the old man 10 minutes after his start.

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