Question

A boat can go 4 km upstream and 10 km downstream in 6 hours. If the speed of stream is 2 km/h, find the speed of boat in still water.

Answer 1

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

Given speed of the stream = 2 km/h.

Upstream speed = x − 2 km/h

Downstream speed = x + 2 km/h

Time to go 4 km upstream:

`4/(x - 2)` hours

Time to go 4 km upstream:

`10/(x+2)` hours

Total time = 6 hours:

`4/(x-2) + 10/(x+2) = 6`

Take LCM (x − 2) (x + 2):

`(4(x+2) + 10 (x-2))/(x^2 - 4) = 6`

4x + 8 + 10x − 20 = 14x − 12

`(14x-12)/(x^2-4) = 6`

14x − 12 = 6x² − 24

6x² − 14x − 12 = 0

Divide by 2:

3x² − 7x − 6 = 0

(3x + 2) (x − 3) = 0

`x = -2/3 or x =3`

The speed of the boat in still water is:

3 km/h​