Question

A man can row at 8 kmph in still water. If the river is running at 2 kmph, it takes him 48
minutes to row to a place and back. How far is the place?
A.. 1 km
B.. 2 km
C.. 3 km
D.. 4 km

Answer 1

Hint: A rate at which a distance is covered by an object within a stipulated time is known as speed. There is a relationship between these three quantities by which we can find the value of a quantity when the other two quantities are given. \[{\text{Speed = }}\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\]
In the case of the river we use these fundamentals only but here speed of the object is dependent upon the speed of the river. If the object is flowing with the stream then the speed of the object increases and decreases if the object is flowing against the stream.


Complete step by step solution:
Speed of man in still water, \[u = 8kmph\]
Speed of the river, \[v = 2kmph\]
Velocity of the boat in downstream, \[u + v = 8 + 2 = 10kmph\]
Velocity of the boat in upstream, \[u - v = 8 - 2 = 6kmph\]
Let us consider the total distance covered by boat is equal to \[x\]
We know \[{\text{Speed = }}\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\], it can also be written as \[{\text{Time = }}\dfrac{{{\text{Distance}}}}{{{\text{Speed}}}}\]
Here given time t=48 minutes is the total time taken by the man to go and come back in his journey, hence we can write it also as \[t = {t_1} + {t_2}\], where \[{t_1}\]is the time taken to reach the destination and \[{t_2}\]is time to come back, so
\[
t = {t_1} + {t_2} \\
t = \dfrac{x}{{10}} + \dfrac{x}{6} \\\dfrac{{48}}{{60}} = \dfrac{{6x + 10x}}{{60}} \\
16x = 48 \\
x = \dfrac{{48}}{16 \\= 3 \\} \\
\]
Hence total time taken to by man to cover the total distance is \[3km\].

Additional Information: Here, the time is given in minutes and the velocity of the boat and stream is given in hours so, it is advisable to the candidates to convert either of the quantities by using the formula \[\left[ {\dfrac{{\text{t}}}{{{\text{60}}}}\left( {{\text{minutes}}} \right){\text{ = hour}}}
\right]\]

Note: If the boat is rowing with the stream (in the direction of stream) it is known as downstream and when the boat is rowing against the stream it is known as upstream. It is to be noted here that, the velocity of upstream and downstream are the velocity of the boat with reference to the ground.