Question

The speed of a boat in still water is $5km/h$. The river is flowing with a speed of $2km/h$ and time taken to cover a certain distance upstream is 2h more than the time taken to cover the same distance downstream. Find the distance
A.10.5 km
B.11 km
C.10.9 km
D.15 km

Answer 1

Hint: First we will assume the value for the distance to be d, now we will find the time taken by boat to travel that particular distance upstream and downstream using the speed as the downstream speed will be the summation of speeds of the boat and river flow and upward will be the difference of their speeds.
Now, we have given the condition on the time taken upstream and downstream solving which we will get the required answer.

Complete step-by-step answer:
Given data: Speed of a boat in still water is $5km/h$.
The speed of the river flow is $5km/h$ .
Time taken to cover a certain distance upstream is 2h more than the time taken to cover the same distance downstream
Let the certain distance that the boat has to travel is d.

As, the downstream speed will be the summation of speeds of the boat and river flow and upstream speed will be the difference of their speeds.
We know that, $time = \dfrac{{dis\tan ce}}{{speed}}$
Therefore, the time taken by boat to cover d distance upstream $ = \dfrac{d}{{5 - 2}}$
Similarly, the time taken by boat to cover d distance downstream $ = \dfrac{d}{{5 + 2}}$
Now it is given that the time taken to cover a certain distance upstream is 2h more than the time taken to cover the same distance downstream
i.e. $\dfrac{d}{{5 - 2}} - \dfrac{d}{{5 + 2}} = 2$
On simplifying the denominator, we get,
  $ \Rightarrow \dfrac{d}{3} - \dfrac{d}{7} = 2$
Multiplying both sides by 21, we get,
  $ \Rightarrow 7d - 3d = 42$
On simplification we get,
  $ \Rightarrow 4d = 42$
On dividing by 4 on both sides we get,
  $\therefore d = 10.5$
Therefore the required distance is 10.5 km
Option(A) is correct.

Note: Always remember that the speed of the river flow given to us is the speed of the river downstream, some students thought of it as the upstream speed and make the mistake of calculating the relative speed and hence getting the wrong answer, so remember this point to make a solution with a correct answer.