Question

A boat takes 6 hours to travel 36 km upstream, and it takes 3 hours to travel 30 km downstream. Find the speed of the boat in still water and the speed of the stream.

Answer 1

Here,

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

And the speed of the stream = y km/h

Then,

Upstream speed = (x − y) km/h

Downstream speed = (x + y) km/h

According to the given condition, forming equations,

(1) The boat takes 6 hours to travel 36 km upstream:

`36/(x - y) = 6`

`x - y = 36/6`

x − y = 6     ...(i)

(2) The boat takes 3 hours to travel 30 km downstream:

`30/(x + y) = 3`

`x + y = 30/3`

x + y = 10     ...(ii)

Now, adding equation (ii) and (i):

(x + y) + (x − y) = 10 + 6

x + x + y − y = 16

2x = 16

x = `16/2`

∴ x = 8

Also, substituting x = 8 in equation (i):

8 − y = 6

y = 8 − 6

∴ y = 2

Hence, the Speed of the boat in still water is 8 km/h, and the Speed of the stream is 2 km/h.