Chapter 6, Problem 8MPS

To determine

To Solve:

The given problem.

Answer to Problem 8MPS

The speed of the current is 3 km/h .

Explanation of Solution

Given:

Given statement is :

A boat travelled 36 km downstream in 2 hours.The return trip upstream took 3 hours.Find the rate of the current.

Calculation:

Let

c = speed of the stream

v = speed of the boat

The relative speed of the boat downstream :

  $v+c=\frac{36}{2}=18km/h\mathrm{................}[speed=\frac{dis\tan ce}{time}]$

The relative speed of the boat upstream :

  $v-c=\frac{36}{3}=12km/h$

Solving both the equations:

  $\begin{array}{l}v+c=\mathrm{18............}(1)\\ v-c=\mathrm{12............}(2)\\ Add(1)and(2):\\ 2v=30\\ \Rightarrow \frac{2v}{2}=\frac{30}{2}\mathrm{..............}[\text{divide each side by 2]}\\ \Rightarrow v=15\\ Substitute\text{ the value of v in equation (1)}\\ \Rightarrow 15+c=18\\ \Rightarrow c=18-\mathrm{15...........}[\text{subtract 15 from each side]}\\ \Rightarrow c=3\end{array}$

So, the speed of the current is 3 km/h and the speed of the boat is 15 km/h.