Question

A boatman goes $2$km against the current of the stream in $1$ hour and goes $1$ km along the current in $10$ min. how long will he take to go $5$ km in stationary water?

Answer 1

At first, we will find out the speed of the boat man along the current. From there we will find the speed in stationary water. Which will be used to find the time required to go in stationary water.

Complete step-by-step answer:
It is given that a boatman goes $2$km against the current of the stream in $1$ hour.
Again, it is given that he goes $1$ km along the current in $10$ min.
Initially, we will find out the speed of the boat man along the current unitary method.
That means we will find out the speed of the boat man along the current in one hour.
We know that, $1$ hour $= 60$min
It is given that in $10$ minutes the boat man covers $1$ km.
So in $1$ min, he will cover $\dfrac{1}{{10}}$ km.
Therefore in $60$ min, he will cover $\dfrac{{60}}{{10}}$ km.
By simplifying we get, the speed of the boat man along the current is $6$km.
Now, we have to find the speed in stationary water.
Let us take, $x$ km/hr. as the speed of the boat in stationary water and $y$ km/hr. as the speed of the current.
According to the problem, we have
$x + y = 6$ …. (1)
$x - y = 2$…. (2)
Adding the equation (1) and (2) we get the value of x,
$x + y + x - y = 6 + 2$
By solving the above equation we get,
$x = \dfrac{8}{2} = 4$ Km/hr.
So, in stationary water, he can go $4$km in one hour.
Therefore, we can find the time required to go 5 km in stationary water using the above speed.
He can cover $4$ km in $60$min.
He can cover $1$ km in $\dfrac{{60}}{4}$min.
He can cover $5$ km in $\dfrac{{60}}{4} \times 5$min.
By simplifying the above term, we get, the required time $= 75$min $= 1hr15\min$
Hence, he will take$1hr15\min$ to go $5$ km in stationary water.

Note: To go against the current, the speed of the boat has to be greater than the speed of the current. But to move along the current it is not required.