SOLUTION: A man rowed 10 km up ariver in 5 hours and back in 21/2 hours. Find the rate of the current and his rate of rowing in still water.

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Question 161731: A man rowed 10 km up ariver in 5 hours and back in 21/2 hours. Find the rate of the current and his rate of rowing in still water.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the rate of the current = c
Let his rate rowing in still water = s
Going upriver is against the current
10%2F%28s+-+c%29+=+5
Going back is with the current
10%2F%28s+%2B+c%29+=+2.5
This is 2 equations and 2 unknowns, so I should
be able to solve
Multiply both sides of the 1st by s+-+c
Multiply both sides of the 2nd by s+%2B+c
(1) 10+=+5%2A%28s+-+c%29
(2) 10+=+2.5%2A%28s+%2B+c%29
----------------------
(1) 10+=+5s+-+5c
(2) 10+=+2.5s+%2B+2.5c
Multiply (2) by 2 and add equations
(1) 10+=+5s+-+5c
(2) 20+=+5s+%2B+5c
30+=+10s
s+=+3 km/hr
And, since
10%2F%28s+-+c%29+=+5
10%2F%283+-+c%29+=+5
10+=+5%2A%283+-+c%29
10+=+15+-+5c
5c+=+5
c+=+1 km/hr
His rate in still water is 3 km/hr and the rate of the
current is 1 km/hr
check:
10%2F%28s+-+c%29+=+5
10%2F%283+-+1%29+=+5
10%2F2+=+5
5+=+5
OK