Question

A boat goes 50 km downstream in the same time that it takes to go 30 km upstream. The speed of the stream is 3km/hour. Find the speed of the boat in still water.

Answer 1

The speed of the boat in still water is 12 km/hour.

Explanation:

Given:

Boat goes 50 km downstream and 30 km upstream. The speed of the stream 3 km/hour.

Now, to find the speed of the boat in still water:

Let the speed of boat in still water be
`x km/hour`.

The speed of the downstream be
`x+3`

And, the speed of the upstream be
`x-3`

And, now we find the time by putting the formula:

`Time = (Distance)/(Rate)`

So, downstream time is:

`downstream\ time = (50)/(x+3)`

So, upstream time is:

`upstream\ time = (30)/(x-3)`

According to question:

Time upstream = Time downstream

`(30)/(x-3) = (50)/(x+3)`

By cross multiplication:

`30* (x+3)= 50* (x-3)`

`30x+90=50x-150`

By taking variables in one side and taking numbers on the other side we get:

`90+150=50x-30x`

`240=20x`

Dividing both sides by 20 we get :

`12=x`

Therefore, the speed of the boat in still water is 12 km/hour.