Question

A boat takes 2 hours to go 24 km downstream and takes 3 hours to return, moving 24 km upstream. Find the speed of the boat in still water.

Answer 1

Here, let:

The speed of the boat in still water is x km/h,

And the speed of the stream is y km/h.

Downstream speed = x + y km/h

Upstream speed = x − y km/h

Forming equations using time = `"distance"/"speed"`,

(i) For downstream:

`24/(x + y) = 2`

`x + y = 24/2`

x + y = 12     ...(1)

(ii) For upstream:

`24/(x - y) = 3`

`x - y = 24/3`

x − y = 8     ...(2)

Adding equation (1) and equation (2):

(x + y) + (x − y) = 12 + 8

2x = 20

x = `20/2`

∴ x = 10

Substitute x = 10 in equation (1):

10 + y = 12

y = 12 − 10

∴ y = 2

Hence, the boat’s speed in still water is 10km/h.