Question

The speed of a stream is 4 mph. A boat travels 3 miles upstream in the same time it takes to travel 11 miles downstream. What is the speed of the boat in Stillwater?

Answer 1

Let the speed in still water be
`x` miles per hour.

The speed upstream will be slower than the speed downstream.

Speed upstream
`= x-4` miles per hour and speed downstream will be
`x+4` miles per hour.

`\text{Time Taken}=\frac{\text{Distance}}{\text{Speed}}`

The time taken for the trip upstream and the trip downstream are the same:

`\text{time}_{\text{up}}=(3)/(x-4)`

`\text{time}_{\text{down}}=(11)/(x+4)`

`(11)/(x+4) =(3)/(x-4) \ \ \ \ \ \ \ \leftarrow \ \text{cross multiply}`

`11(x-4)=3(x+4)`

`11x-44=3x+12`

`11x-3x=12+44`

`8x=56`

`\bold{x=7}` miles per hour