A boat traveled 96 miles in 8 hours against the current The

A boat traveled 96 miles in 8 hours against the current. The boat returned to its starting point following the saame course traveling with the current. The return trip took 5 hours. What is the speed of the current and the speed of the boat in still water?

Solution

Let y be the current and let x be the boat;s speed
8(x-y)=96 -----> 8x-8y=96 (equation 1 )
5(x+y)=96 -----> 5x+5y=96 (equation 2 )

Mutliply equation 1 by 5 -----> 40x-40y=480
Multiply equation 2 by 8 -----> 40x+40y=768
Add the equations:

80x=1248
x=15.6
5(15.6)+5y=96
78+5y=96
5y=18
y=3.6

Hence the speed of the boat is 15.6mph and the speed of the current is 3.6mph.