SOLUTION: A man who can row 4 miles per hour in still water finds that it requires 6 1/2 hours to row upstream a distance requiring 3 1/4 to row downstream. what is the rate of the stream?

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Question 774924: A man who can row 4 miles per hour in still water finds that it requires 6 1/2 hours to row upstream a distance requiring 3 1/4 to row downstream. what is the rate of the stream?
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Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This type of uniform rates problem comes up so frequently that a more general solution is valuable.
A man can row R miles per hour in still water needs g hours to row upsteam for distance d and requires b hours to row that same distance back downsteam. Find the rate of the stream, c.

R = row rate in still water.
c = rate of stream.
g = time to travel d distance upstream.
b = time to travel d distance downstream.
d = each one-way distance up and back destination.
INQUIRY FOR UNKNOWN VARIABLE, c.
INTERMEDIATE UNKNOWN VARIABLE, d.

ORGANIZE DATA INTO TABLE

Direction_______rate_________time__________distance
Up______________R-c__________g_____________d=(R-c)g
Back____________R+c__________b_____________d=(R+c)b

The distance going up to the destination, upstream is equal to the distance returning back downstream. In this general case, observe that R-c%3CR%2Bc and that this is in agreement with g%3Eb.

The equality of the two distances indicates highlight%28%28R-c%29g=%28R%2Bc%29b%29.
We solve this equation for the unknown number, c.