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 \frac{k m}{h r}

hr

km

and speed of water current is 4 \frac{k m}{h r}

hr

km

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 \frac{k m}{h r}

hr

km

And speed of water current =v \frac{k m}{h r}

hr

km

Speed downstream = (u + v) \frac{k m}{h r}

hr

km

Speed upstream = (u - v) \frac{k m}{h r}

hr

km

\begin{gathered}\begin{array}{l}{ \frac{16}{u-v}+\frac{24}{u+v}=6 arrow(1)}\\ \\ {\frac{12}{u-v}+\frac{36}{u+v}=6 arrow(2)}\\ \\ {\text { Let } \frac{1}{u-v}=x, \frac{1}{u-v}=y}\end{array}\end{gathered}

u−v

16

+

u+v

24

=6arrow(1)

u−v

12

+

u+v

36

=6arrow(2)

Let

u−v

1

=x,

u−v

1

=y

Substitute in equation (1), 16 x+24 y=6 arrow(3)16x+24y=6arrow(3)

Substitute in equation (2), 12 x+36 y=6 arrow(4)12x+36y=6arrow(4)

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

72y = 6

y= \frac{1}{12}

12

1

, substitute in equation (3), we get x = \frac{1}{4}=

4

1

Hence u – v = 4, u + v = 12

Adding these equations we get u = 8\ \frac{k m}{h r}8

hr

km

, then v =4\ \frac{k m}{h r}4

hr

km