Question 215095
It took a patrol boat 5 hours to travel 60km up a river against the current,
 and 3 hours for the return trip with the current.
 Find the speed of the boat in still water and the speed of the current
:
Let s = boat speed in still water
Let c = speed of the current
then
(s+c) = speed down river (with the current)
and
(s-c) = speed up river (against the current)
:
Write two distance equations, Dist = time * speed
3(s + c) = 60; down river
5(s - c) = 60; up-river
;
We can simplify both these equations
Divide the 1st by 3 and the 2nd equation by 5, results
s + c = 20
s - c = 12
-------------addition eliminates c find s
2s = 32
s = {{{32/2}}}
s = 16 mph is the speed in still water
:
Find c using eq: s + c = 20
16 + c = 20
c = 20 - 16
c = 4 mph is the speed of the current
:
:
Check solution in the 2nd original equation
5(16 - 4) =
5(12) = 60 mi