Question

A boat traveled 96 miles downstream and back. The trip downstream took 4 hours. The trip back took 12 hours. Find the speed of the boat in still water and the speed of the current

Answer 1

Speed of boat is still water: 16 miles per hour.

Speed of current: 8 miles per hour.

Explanation:

Let x represent speed of boat in still water and y represent speed of current.

Downstream speed would be
`x+y`.

Upstream speed would be
`x-y`.

We have been given that a boat traveled 96 miles downstream and back. The trip downstream took 4 hours.

`\text{Rate}=\frac{\text{Distance}}{\text{Time}}`

`x+y=(96)/(4)...(1)`

`x+y=24...(1)`

We are also told that the trip back took 12 hours. We can represent this information in an equation as:

`x-y=(96)/(12)...(2)`

`x-y=8...(2)`

Upon adding equation (1) and equation (2), we will get:

`x+x+y-y=24+8`

`2x=32`

`(2x)/(2)=(32)/(2)`

`x=16`

Therefore, the speed of boat in the still water is 16 miles per hour.

Upon substituting
`x=16` in equation (1), we will get:

`16+y=24`

`16-16+y=24-16`

`y=8`

Therefore, the speed of the current is 8 miles per hour.