Question

A motorboat takes 4 hours to travel 128 mi going upstream. the return trip takes 2 hours going downstream. what is the rate of the boat in still water and what is the rate of the current

Answer 1

First, find the MPH he was going at to go upstream which would be 128/4 or 32 mph to go upstream and twice as much to go downstream
We can now construct a system of equations where x = the speed of the both and y = the current...
Going upstream: x - y = 32
Going downstream: x + y = 64
Solve this system of equations!
x - y = 32
x = 32 + y
(32 + y) + y = 64
2y + 32 = 64
2y = 32
y = 16
Subtitute 16 for y in the first equation...
x - 16 = 32
x = 48
Rate of the boat in still water = 48mph
Rate of the current = 16 mph