a boat traveled 160 miles downstream and back. the trip downstream took 8 hours. the trip back took 40 hours. find the speed of the boat in still water and the speed if the current

Let speed of the boat in still water = x miles per hour

Let speed of the current = y miles per hour

When water and current both flow in same direction then effective speed will be sum of both speeds that is (x+y)

now plug the given values in formula speed=distance/time

we get equation:

(x+y) = 160/8

or x+y=20 ... (i)

When water and current both flow in opposite direction then effective speed will be difference of both speeds that is (x-y)

now plug the given values in formula speed=distance/time

we get equation:

(x-y) = 160/40

or x-y=4

or x=4+y ... (ii)

plug value of x into (i)

4+y+y=20

4+2y=20

2y=16

y=8

plug value of y into (ii)

x=4+8=12

Hence final answer is given by:

Speed of the boat in still water = 12 miles per hour

Speed of the current = 8 miles per hour