Question

The speed of a motor boat in still water 20 km/ hr and river flow is 5 km/ hr. A float is dropped from the boat when it starts moving upstream. After moving 1.5 km the boat returns back. The boat will catch the float (from initial instant) after:
(A) 6 min
(B) 12 min
(C) 10 min
(D) 15 min

Answer 1

Hint: To answer this question we should at first find the time that is taken by the boat to speed in the upstream. For this we have to consider the speed of the boat in the upstream and the distance that is already mentioned. Next we have to find the time taken by the boat when the speed and distance is considered with respect to the boat. This will give us the answer to the required question.

Complete step by step answer:
We should know that the speed of boat in upstream = 15 km/ hr
The distance that we are given is 1.5 km.
The time let be considered as ${t_1}$. The value of ${t_1}$ is given as:
${t_1} = \dfrac{{1.5}}{{15}} = 6\min $
So now we have to find the distance moved by float in this time. So the distance is:
$5 \times \dfrac{1}{{10}} = \dfrac{1}{2}km$
Now we have to consider the speed of the boat with respect to the float which is 20 km/ hr.
So the time let it be considered as ${t_2}$. The value of ${t_2}$ is:
$\dfrac{{2km}}{{20}} = 6\min $
So we can say that the boat will catch the float (from initial instant) after 6 min.

So the correct answer is option A.

Note: In this question we have come across the term upstream, to avoid any difficulty we need to define this term. By upstream we mean when the boat moves in a direction which is opposite to the direction of the stream. Similarly, if the boat would move in a direction which is similar to that of the direction of the stream then it would have called downstream.