Question

a motorboat goes downstream in a river and covers the distance between two coastal towns in five hours it covers this distance upstream in six hours if the speed of the stream is 2km/h, find the speed of the boat in still water

Answer 1

Let the speed of boat in still water be "x" km/hr and the distance between the two coastal towns be "d" km.
Then,
Downstream:
$\frac{d}{x+2} = 5$

Upstream:
$\frac{d}{x-2} = 6$

x = 22 km/hr

Answer 2

Since we have to find the speed of the boat in

still water, let us suppose that it is

x km/h.

This means that while going downstream the

speed of the boat will be (x + 2) kmph

because the water current is pushing the boat

at 2 kmph in addition to its own speed

‘x’kmph.

Now the speed of the boat down stream = (x + 2) kmph

⇒ distance covered in 1 hour = x + 2 km.

∴ distance covered in 5 hours = 5 (x + 2) km

Hence the distance between A and B is 5 (x + 2) km

But while going upstream the boat has to work against the water current.

Therefore its speed upstream will be (x – 2) kmph.

⇒ Distance covered in 1 hour = (x – 2) km

Distance covered in 6 hours = 6 (x – 2) km

∴ distance between A and B is 6 (x – 2) km

But the distance between A and B is fixed

∴ 5 (x + 2) = 6 (x – 2)

⇒ 5x + 10 = 6x – 12

⇒ 5x – 6x = –12 – 10

∴ –x = –22

x = 22.

Therefore speed of the boat in still water is 22 kmph.