Question

A boat goes 16 km upstream and 24 km downstream in 6 hours also it covers 12 km upstream and 36 km downstream in same time find the speed of boat and water current. Answer of this question

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Speed of boat is 8 $\frac{k m}{h r}$ and speed of water current is 4 $\frac{k m}{h r}$

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 $\frac{k m}{h r}$

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

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

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

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

Substitute in equation (1), $16 x+24 y=6 \rightarrow(3)$

Substitute in equation (2), $12 x+36 y=6 \rightarrow(4)$

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 = $8\ \frac{k m}{h r}$, then v =$4\ \frac{k m}{h r}$