Question

It has been given that a motorboat is covering a particular distance in $6h$ moving downstream on a river. It will be covering the identical distance in $10h$ moving upstream. What will be the time it will be taking in order to cover the similar distance in still water?
$\begin{align}
  & A.6.5h \\
 & B.8h \\
 & C.9h \\
 & D.7.5h \\
\end{align}$

Answer 1

Hint: The distance covered will be equivalent to the product of the time taken in order to move downstream on a river and the sum of the velocity of the water and the velocity in the still water. The distance covered will be equivalent to the product of the time taken in order to move upstream on a river and the difference of the velocity in the still water and the velocity of the water. This will help you in answering this question.

Complete answer:
Let us assume that the velocity in the still water is $S$. The velocity of the water can be mentioned as $W$. The distance which has been covered in this situation can be written as $D$.
The distance covered will be equivalent to the product of the time taken in order to move downstream on a river and the sum of the velocity of the water and the velocity in the still water. This can be written as an equation given as,
$D=6\left( S+W \right)$
The distance covered will be equivalent to the product of the time taken in order to move upstream on a river and the difference of the velocity in the still water and the velocity of the water. This can be written as,
\[D=10\left( S-W \right)\]
As this distance covered has mentioned to be equivalent, we can write that,
\[6\left( S+W \right)=10\left( S-W \right)\]
Simplifying this equation can be shown as,
\[S=4W\]
Therefore the distance covered can be obtained as,
\[D=7.5hr\]
Therefore the correct answer for the question has been found.

This has been mentioned as option D.

Note:
The velocity of a body can be defined as the variation of the displacement of the body with respect to the time taken. The displacement of the body can be found by taking the perpendicular distance between the initial and final position of the body. Both these quantities are found to be vectors.