Question

A motorboat goes 36 km downstream in the same amount of time that it takes to go 24 km upstream. If the current is flowing at 3 km/h, what is the rate of the boat in still water?

Answer 1

Speed of boat in still water = 15 km/hr

Explanation:

Let the speed of the boat in still water = x km/hr

Speed of the stream = 3km/hr

Then effective speed of the boat when travelling upstream = x-3 km/hr

Effective speed of the boat when travelling downstream = x+3 km/hr

Time taken for traveling 36 km downstream = Time taken for traveling 24 km upstream

=>
`\[(36)/(x+3)=(24)/(x-3)\]`

=>
`\[36*(x-3)=24*(x+3)\]`

=>
`\[36x - 108 = 24x +72\]`

=>
`\[36x - 24x = 108 + 72\]`

=>
`\[12x = 180\]`

=> x=15