Question

A motorboat takes 5 hours to travel 150 miles going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Rate of the boat in still water:

Rate of the current:

Answer 1

The rate of the boat in still water is 40 miles per hour

The rate of the current is 10 miles per hour

Explanation:

we know that

The speed or rate is equal to divide the distance by the time

Let

x ----> the rate of the current (miles per hour)

y ----> the rate of the boat in still water (miles per hour)

we have that

going upstream

`y-x=(150)/(5)`

`y-x=30` ----> equation A

going downstream

`y+x=(150)/(3)`

`y+x=50` ----> equation B

Solve the system of equations by elimination

Adds equation A and equation B

`y-x=30\\y+x=50\\------\\y+y=30+50\\2y=80\\y=40`

Find the value of x

`y+x=50`

`40+x=50`

`x=10`

therefore

The rate of the boat in still water is 40 miles per hour

The rate of the current is 10 miles per hour