Julie and Eric row their boat at a constant speed 45 miles d

Julie and Eric row their boat (at a constant speed) 45 miles downstream for 5
hours, helped by the current. Rowing at the same rate, the trip back against
the current takes 9 hours. Find the rate of the current.

Solution

Let s = speed of the boat in still water
Let c = rate of the current
Then
(s-c) = speed upstream
(s+c) = speed downstream
:
Write two distance equation, use elimination
5(s+c) = 45
9(s-c) = 45
Simplify, divide 1st equation by 5, 2nd equation by 9; results
s + c = 9
s - c = 5
-----------Subtraction eliminates s, find c
2c = 4
c = 2 mph is the current
:
:
Check solution:
Find s:
s + 2 = 9
s = 9-2
s = 7 mph in still water
:
Check solution in original upstream equation:
9(7-2) = 45