SOLUTION: In still water a boat averages 8 mph it takes the same amount of time to travel 22 miles downstream with the same current as 10 miles upstream against the current whats the rate of

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Question 761617: In still water a boat averages 8 mph it takes the same amount of time to travel 22 miles downstream with the same current as 10 miles upstream against the current whats the rate of the water current
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Distance = Rate x Time
D+=+R%2AT
Solve the equation for T by dividing both sides by R
T+=+D%2FR
----------------
Let C = the rate of the water current.
The downstream rate is then 8mph + C
and the upstream rate is 8mpH - C.
Since T (The time), is the same in both the upstream and downstream equations, you can set the Distance/Rate ratio equal to each other and solve for C
22%2F%288+%2B+C%29+=+10%2F%288+-+C%29
Multiply both sides by (8+C) and (8-C).

Simplify
22%2A%288-C%29+=+10%2A%288%2BC%29
Multiply through.
176+-+22C+=+80+%2B+10C
Add 22C to both sides.
176+=+80+%2B+32C
Subtract 80 from both sides.
96+=+32C
Divide both sides by 32.
highlight%283+=+C%29
The current of the water is 3mph