Question 288541
A motorboat takes 4 hours to travel 256 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?

let speed of the boat in still water be x

let the speed of the current be y

upstream speed of boat is x-y

distance is 256

time is 4 hours

256 / x-y =4

Down stream

speed of boat = x+y

distance = 256

256/ x+y = 2

4x-4y=256------------1

2x+2y=256------------2

multiply eq 2 by 2

4x+4y=512-----------3

Add eq 1 & 3

4x-4y+4x+4y=512+512

8x=1024

x= 1024/8

=128 mph

plug the value of x in eq1

we get y=64mph  speed of the current