# A man rowed up a river 10 miles in 5 hours and back in 2.5 hours. Find the rate of the current and his rate of rowing in still water.

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A man rows up a river 10 miles in 5 hours and the return trip requires 2.5 hours.

Use the relationship d=rt where d is distance, r is the rate, and t is the time.

Let x be the man's rowing speed, and y be the speed of the current.

(1) Going upriver (against the current) we have 10=(x-y)5 or 10=5x-5y

(2) Going downriver (with the current) we have 10=(x+y)2.5 or 10=2.5x+2.5y

We now have a system of linear equations in 2 variables:

5x-5y=10

2.5x+2.5y=10

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Multiply the second equation by 2 to get:

5x-5y=10

5x+5y=20

Adding the equations we get:

10x=30 ==> x=3

Substituting for x we get 15-5y=10 ==> 5y=5 ==> y=1

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**The man's rowing speed is 3mph and the current is 1mph**

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Check: going upriver the actual speed is 2mph (rowing speed minus current); traveling 2mph for 5 hours gives a distance of 10 miles.

Going downriver the effective speed is 4mph (the rowing speed plus the current); traveling 4mph for 2.5hours gives a distance of 10 miles.