Question

A man can row \[14\] \[km/h\] in still water. In the stream following with the speed of \[10\] \[km/h\] he takes 4 hours to move with the stream and come back. Find the distance he rowed the boat.

Answer 1

Hint: First we take the distance he rowed the boat be D.
The given data are boat speed in water \[=14\] \[km/h\], stream speed in water \[=10\] \[km/h\]
Also he takes 4 hours to move with the stream and come back.
We find distance using the formula \[Time = \dfrac{{Distance}}{{Speed}}\] , which means time is equal to the distance divided by speed.

Complete step-by-step answer: Let D be the distance he rowed the boat.
In water, the direction against the stream is called upstream so we subtract both speeds.
We get, boat speed in upstream \[ = 14 - 10 = 4km/h\]
In water, the direction along the stream is called downstream so we added both speeds.
We get, boat speed in downstream\[ = 14 + 10 = 24km/h\]
\[Time = \dfrac{{Distance}}{{Speed}}\]
Time taken in upstream \[ = \dfrac{D}{4}\]
Time taken in downstream \[ = \dfrac{D}{{24}}\]
It is given that the time taken in upstream and downstream are added is equal to 4 hours.
That is, Time taken in upstream + time taken in downstream \[ = 4\]
Substituting the above values we get
\[\dfrac{D}{4} + \dfrac{D}{{24}} = 4\]
Taking LCM of 4 and 24, also evaluate that
\[\dfrac{{6D + D}}{{24}} = 4\]
This in turn implies that we get,
\[\begin{gathered}
  7D = 96 \\
  D = \dfrac{{96}}{7} \\
\end{gathered} \]
\[D = 13.71\]Km

Therefore, the distance he rowed the boat \[D = 13.71\] km

Note: In water, the direction along the stream is called downstream so we added both speeds.
And, the direction against the stream is called upstream so we subtracted both speeds.
The time taken in upstream and downstream are added is equal to 4 hours.