Question

The speed of a boat in still water is 9 km per hour. If the boat goes 54 km downstream in 4 hours, find the speed of the stream.
A. \[2.5{\text{ km/hr}}\]
B. \[4.5{\text{ km/hr}}\]
C. \[3.7{\text{ km/hr}}\]
D. \[5.7{\text{ km/hr}}\]

Answer 1

Hint: First we will assume that the speed of the stream is represented by \[x\] km per hour and then compute the speed of the boat downstream by adding the speed of the boat with the speed of the stream. Then we will use the formula to calculate the speed of the boat downstream,\[\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\] and then substitute the value of distance, speed, and time in the above formula of the speed of boat downstream.

Complete step by step answer:

We are given that the speed of a boat in still water is 9 km per hour.

Let us assume that the speed of the stream is represented by \[x\] km per hour.

First, we will compute the speed of the boat downstream by adding the speed of the boat with the speed of the stream, we get

\[ \Rightarrow \left( {9 + x} \right){\text{km/hr}}\]

Since we are given that the distance covered by boat in 4 hours downstream goes 54 km.

We know that the speed of the boat downstream is calculated using the formula,\[\dfrac{{{\text{Distance}}}}{{{\text{Time}}}}\].
Substituting the value of distance, speed, and time in the above formula of the speed of boat downstream, we get

\[ \Rightarrow 9 + x = \dfrac{{54}}{4}\]

Multiplying the above equation by 4 on both sides, we get

\[
   \Rightarrow 4\left( {9 + x} \right) = 4\left( {\dfrac{{54}}{4}} \right) \\
   \Rightarrow 36 + 4x = 54 \\
 \]

Subtracting the above equation by 36 on each side, we get

\[
   \Rightarrow 36 + 4x - 36 = 54 - 36 \\
   \Rightarrow 4x = 18 \\
 \]

Dividing the above equation by 4 on both sides, we get

\[
   \Rightarrow \dfrac{{4x}}{4} = \dfrac{{18}}{4} \\
   \Rightarrow x = 4.5{\text{ km/hr}} \\
 \]

Thus, the speed of the stream is \[4.5{\text{ km/hr}}\].
Hence, option B is correct.

Note: In solving these types of questions, students should be careful while forming the expression of speed of upstream and downstream respectively. Also, the final answer, which the student obtained must write the units properly.