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

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