a boat travels 12 miles downstream in 15 hours on the return

a boat travels 12 miles downstream in 1.5 hours. on the return trip the boat travles the same distance upstream in 2 hours. find the rate of the boat in still water and the rate of the current

Solution

Let the speed of the boat be x
Let the speed of the current be y

1.5(x+y)=12---->1.5x+1.5y=12 (1)
solve for y in there.
1.5y=12-1.5x
y=8-x (subsitution)

second equation:
2(x-y)=12
2x-2y=12
Subsitute for y
2x-2(8-x)=12
2x-16+2x=12
4x=28
x=7

y=8-7
y=1

Hence, the speed of the boat is 7mph and the speed of the current 1mph.