Question 28317
The thing that stays the same for both trips is elapsed time

Solve the rate formula for t
time = distance / rate
The times are equal, so
{{{distance[1] / rate[1] = distance[2] / rate[2]}}}
The rate for downstream is the rate in still water + rate of the current
The rate for upstream is the rate in still water - rate of the current
Fill in the values
Call the rate in still water r
{{{52 / (r + 4) = 26 / (r - 4)}}}
Cross multiply
{{{26*r + 104 = 52*r - 208}}}
{{{26*r = 312}}}
{{{r = 12}}}
So, the speed in still water is 12 mph
Check by plugging into equation
{{{52 / (12 + 4) = 26 / (12 - 4)}}}
{{{52 / 16 = 26 / 8}}}
{{{13/4 = 13/4}}}
Checks