UNO High School Problem of the Week Competition

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Problem 5



Two men at points R and S, 76 miles apart, set out at the same time to walk towards each other. The man at R walks uniformly at the rate of 4 1/2 miles per hour; the man at S walks at the constant rate of 3 1/4 miles per hour for the first hour, at 3 3/4 miles per hour for the second hour, and so on, in arithmetic progression.
The men will meet x miles nearer R than S, find x.

Solution