Question

A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.

Answer 1

We know that Speed = Distance / Time. This means Time = Distance / Speed

Let "u" be speed upstream and "d" be speed downstream

Using this we get:
30/u + 28/d = 7 ------------- (i)

We are also given that the boat can travel up and down in 5 hours. This means:
21/u + 21/d = 5 ------------- (ii)

Multiplying (ii) by 30/21, we get
30/u + 30/d = 50/7 --------- (iii)

Subtracting (iii) from (i), we get:
d = 14 km/hr

Inputting this in equation (i), we get u = 6 km/hr

We know that Speed Upstream = Speed of boat - Speed of stream
and Speed Downstream = Speed of boat + Speed of stream

From here we get two more equations:
u = Sb - Sr, this means: 6 = Sb - Sr ----------- (iv)
and
d = Sb+Sr, this means: 14 = Sb + Sr ------------- (v)

Adding (iv) and (v), we get:
Sb = 10 km/hr; substituting this value in equation (iv) we get
Sr = 4 km/hr

Please note, Sb = Speed of boat in still water and Sr = speed of stream.