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

12 km/h

Explanation:

Given: Distance covered by boat downstream = 50 km

Distance covered by boat upstream = 30 km

Time taken by boat in down stream and upstream are equal.

Speed of the stream = 3 km/h

Let x be the speed of boat in still water.

∴ Speed of boat in downstream
`(s_1)` =
`(x+3)\ km/h`

Speed of boat in upstream
`(s_2)` =
`(x-3)\ km/h`

As we know,
`Time = (Distance)/(speed)`

And time remain same for both upstream and downstream

∴
`(50)/((x+3)) = (30)/((x-3))`

Now, cross multiply both side

⇒
`50* (x-3) = 30* (x+3)`

⇒
`50x-30x = 150+90`

∴
`x= 12\ km/h`

∴ Speed of boat in still water is 12 km/h