Question

A motorboat covers a distance of 16km upstream and 24km downstream
in 6 hours. In the same time it covers a distance of 12 km upstream and
36km downstream. Find the speed of the boat in still water and that of the
stream.​

Answer 1

Answer :

Speed of boat is 8 km/hr and speed of water current is 4 km/hr

Given:

Speed of boat in upstream is 16 km

Speed of boat in downstream is 6 km

In 6 hours, the distance covered in upstream is 12km and downstream is 36km

To find:

The boat speed and water current

Solution:

Consider that speed of boat = u km/hr

And speed of water current =v km/hr

Speed downstream = (u + v) km/hr

Speed upstream = (u - v) km/hr

${ \frac{16}{u-v}+\frac{24}{u+v}=6 → (1)}\\ \\ {\frac{12}{u-v}+\frac{36}{u+v}=6 →(2)}\\ \\ {\text { Let } \frac{1}{u-v}=x, \frac{1}{u+v}=y}$

Substitute in equation (1),

16x + 24y = 6 ↦(3)

Substitute in equation (2),

12x + 36y = 6 ↦(4)

Multiplying equation (3) by 4 and equation (4) by 3, we get,

72y = 6

y= $\frac{1}{12}$

substitute in equation (3)

we get x =$\frac{1}{4}$

Hence u – v = 4, u + v = 12

Adding these equations we get,

u = 8 km/hr

v = 4 km/hr