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 still​ water?

Answer 1

`7` miles per hour in still water.

Explanation:

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

The speed upsteam will be slower than the speed downstream.

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

`"Time taken " = "Distance"/"Speed"`

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

`"time"_"up" = 3/(x-4)`

`"time"_"down" = 11/(x+4)`

`11/(x+4) = 3/(x-4)" "larr` cross multiply

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

`11x-44 =3x+12`

`11x-3x = 12+44`

`8x = 56`

`x=7` miles per hour

The trip takes `1` hour in both directions.