Question

A man can row the boat at $5\,km/hr$ in still water. If the velocity of the current is $1\,km/hr$ and it takes him $1\,hour$ to row to a place and come back, how far is the place?
A) $2.5\,km$
B) $3\,km$
C) $2.4\,km$
D) $3.6\,km$

Answer 1

Hint: When the boat is travelling in the direction of speed of the current then the boat is said to go in the downstream. In downstream the speed of the boat is high compared to the normal speed because the water current speed also pushes the boat in the same direction.
When the boat is travelling against the speed of the current then the boat is said to go in the upstream. In upstream, the speed of the boat is low compared to the normal speed because the boat will go against the flow of water.
we will first evaluate the speed of the boat in downstream and upstream and then use these speeds to calculate the required answer by using the relation between time, speed and distance.

Complete step-by-step answer:
We are given that the speed of the boat is $5\,km/hr$ in still water and velocity of the current is $1\,km/hr$. Also, it takes him $1\,hour$ to row to a place and come back.
First, we let the distance of the place be $x\,km$.
Once the distance will be covered in the upstream and other times it will be covered in the downstream.
Now, we evaluate the speed of downstream and the speed of the upstream.
The Speed of the downstream is the sum of the speed of the boat and speed of the current.
Therefore, it will be $5 + 1 = 6\,km/h$
The Speed of the upstream is the difference in the speed of the boat and speed of the current.
Therefore, it will be $5 - 1 = 4\,km/h$
Time is the ratio of distance to speed.
Time taken to cover the distance in upstream is $\dfrac{x}{4}\,hour$
Time taken to cover the distance in downstream is $\dfrac{x}{6}\,hour$
The total time is $1\,hour$.
Therefore,
\[\dfrac{x}{4} + \dfrac{x}{6} = 1\]
Solve the equation by taking LCM and evaluate the value of $x$.
$
  \dfrac{{3x + 2x}}{{12}} = 1 \\
  \dfrac{{5x}}{{12}} = 1 \\
  5x = 12 \\
  x = \dfrac{{12}}{5} \\
  x = 2.4\,km \\
 $

Hence, the distance of the place is $2.4\,km$. Therefore, option (C) is correct.

Note:
While solving the kind of problems on boats and streams, think clearly and imagine where the speed of boat will vary in downstream and upstream. Then it will be easy to solve the problem using simple arithmetic operations and time, speed and distance formula.