Question

Ritu can row downstream \[20\]km in \[2\]hours, and upstream \[4\]km in \[2\]hours. Find her speed of rowing in still water and the speed of the current.
(A) \[6,4\]
(B) \[4,6\]
(C) \[8,12\]
(D) None of these

Answer 1

Hint: We should remember that downstream will be in the direction of flow and upstream will be opposite to the direction of flow. After knowing this, it will be easy for us to solve the question. We take two cases here and then we will form two equations and then the values of ‘x’ and ‘y’ will come after solving the equations.

Complete step by step answer:
Stream is known as the moving water in the river. Downstream is the case when the boat moves along the direction of the speed, while upstream is the condition when the boat moves opposite to the direction of the stream and for upstream and downstream, net speed will be the final speed of the boat.
Let the speed of the boat be $x{km}/{h}\;$ and the speed of current be$y{km}/{h}\;$
Case 1: For downstream.
It is given that
$\text{distance}=20\text{ }km$
Time taken to go downstream is given as:
$Time=2hours$
Now in the question,
If the speed of boat is$x{km}/{h}\;$ and the speed of current is $y{km}/{h}\;$ then the speed of downstream will be given by,
 \[\Rightarrow speed\text{ }of\text{ }downstream=x+y\]
We know that, the formula of speed is given by,
\[\Rightarrow speed=\dfrac{d}{t}\]………eq (1)
Now putting the values of distance, speed and time in the eq (1), we get
\[\Rightarrow x+y=\dfrac{20}{2}\]
\[\Rightarrow x+y=10\]……….eq (2)
Case 2: For upstream
 It is given that,
$\text{distance}=4km$
Time taken to go upstream is given as:
$Time=2\text{ }hours$
Now to the question.
If the speed of boat is$x{km}/{h}\;$ and the speed of current is$y{km}/{h}\;$ then the speed of upstream will be given as:
$\Rightarrow speed\text{ }of\text{ }upstream=x-y$
On putting the above values in eq(1), we get
\[\Rightarrow x-y=\dfrac{4}{2}\]
\[\Rightarrow x-y=2\]……..eq (3)
Now we will solve eq (2) and eq (3) to find out the value of x and y.
We can write the eq(3) as:
  \[\Rightarrow x=2+y\]…………….eq(4)
On putting the value of x in eq (2) , we get
 \[\begin{align}
  & \Rightarrow 2+y+y=10 \\
 & \Rightarrow 2+2y=10 \\
 & \Rightarrow 2y=8 \\
 & \Rightarrow y=4 \\
\end{align}\]
Now after finding the value of y, we will put the value of y in eq (4), to find out the value of x which is given as:
$\begin{align}
 & \Rightarrow x=4+2 \\
 & \Rightarrow x=6 \\
\end{align}$
So , the speeds are given as:
\[\begin{align}
  & \Rightarrow speed\text{ }of\text{ }boat=6{km}/{h}\; \\
 & \Rightarrow speed\text{ }of\text{ }current=4{km}/{h}\; \\
\end{align}\]

So, the correct answer is “Option A”.

Note: The speed of still water is always equal to zero. The speed of the boat with respect to the bank of the river is known as the rate of flow of water. We should remember that if the direction of the boat and the stream is the same then the speed will be added and if the direction of the boat and stream is opposite then speed will be subtracted.