Question 774924
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<R+c}}} and that this is in agreement with {{{g>b}}}.


The equality of the two distances indicates {{{highlight((R-c)g=(R+c)b)}}}.
We solve this equation for the unknown number, c.