Question

A boat can travel with a speed of $22km h{{r}^{-1}}$ in still water. If the speed of the stream is $8kmh{{r}^{-1}}$, find time taken by it to go $135km$ downstream.
$\begin{align}
  & A.9\dfrac{1}{2}hr \\
 & B.5\dfrac{7}{2}hr \\
 & C.8\dfrac{4}{5}hr \\
 & D.4\dfrac{1}{2}hr \\
\end{align}$

Answer 1

Hint: The concept of relative velocity should be taken here in order to solve this question. First of all find out the speed of boat in downstream which is the direction of water, then find speed of boat in return also. Then the time taken for the travel should be calculated in both the direction of downstream and also for the return journey. Now calculate the total time taken.

Complete answer:
first of all let us look what all have been given in the question,
The speed of boat in still water can be written as,
${{V}_{b}}=22kmh{{r}^{-1}}$
The speed of water stream is given as,
${{V}_{w}}=8kmh{{r}^{-1}}$


 

Firstly the boat is travelling in the downstream which is the direction of flow of water also. Therefore the velocity of the flow will be,
 ${{V}_{d}}=\left( 22+8 \right)kmh{{r}^{-1}}=30kmh{{r}^{-1}}$
Secondly the boat is returning to the initial position. In this case the boat will be travelling in the opposite direction of flow of water stream.
${{V}_{r}}=\left( 22-8 \right)kmh{{r}^{-1}}=14kmh{{r}^{-1}}$
The time taken to travel in the downstream, which covers a distance of$135km$.
${{t}_{d}}=\dfrac{135}{30}hr=4.5hr$
And the time taken to travel in return to its initial state covering the same distance will be,
${{t}_{r}}=\dfrac{135}{14}hr$
That is the body is taking a time interval of $4.5hr$ in order to travel a distance of $135km$ downstream.

So, the correct answer is “Option D”.

Note:
In the case of water, the direction in the same direction of the water stream is known as the downstream. And if the direction is against the water stream, then it is called upstream. Sometimes the wind also plays an important role in the speed of the boat in water bodies. So when we solve, these all should be in mind as well.