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Skating Dynamics (Posted on 2024-05-23)

A father and his son are skating around a circular skating rink. From time to time, the father overtakes the son. After the son starts skating in the opposite direction, they begin to meet five times more often. What is the ratio of the skating speeds of the father and the son?

No Solution Yet Submitted by Danish Ahmed Khan

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| Comment 2 of 3 |

Seeing Charlie's note, I interpreted "five times more often" the second way.

d = rink circumference

R,r are father's and son's speeds

5T = time between meetings when same direction

T = time between meetings when opposite direction

Same direction:

Son's dist is x = 5rT

Father's dist is d+x = 5RT

d + 5rT = 5RT

d = 5RT - 5rT = 5T(R-r)

Opposite direction:

Son's dist is x = rT

Father's dist is d-x = RT

d - rT = RT

d = RT + rT = T(R+r)

5RT - 5rT = RT + rT

4R = 6r

R/r = 3/2

Posted by Larry on 2024-05-23 09:17:39

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