Question

A motor boat covers 36 km downstream and 24 km upstream. If the boat takes 6 hours to cover each distance, then the speed of the motor boat in still water is.

• A. 1km/hr
• B. 4km/hr
• C. 8km/hr
• D. 5km/hr

Answer 1

The Correct Option is D

To solve the problem, we need to determine the speed of the motor boat in still water. Let's denote:

• \(v_b\): Speed of the boat in still water (in km/hr)
• \(v_s\): Speed of the stream (in km/hr)

In downstream, the effective speed of the boat is \(v_b+v_s\), and it covers 36 km. Time is given as 6 hours, so we can write the equation:

\(v_b+v_s=\frac{36}{6}=6 \text{ km/hr}\)

In upstream, the effective speed of the boat is \(v_b-v_s\), and it covers 24 km. Time is also given as 6 hours, so we can write:

\(v_b-v_s=\frac{24}{6}=4 \text{ km/hr}\)

We have two equations:

1. \(v_b+v_s=6\)
2. \(v_b-v_s=4\)

By adding these two equations, we eliminate \(v_s\):

\((v_b+v_s)+(v_b-v_s)=6+4\)

\(2v_b=10\)

Solving for \(v_b\), we get:

\(v_b=\frac{10}{2}=5 \text{ km/hr}\)

The speed of the motor boat in still water is 5 km/hr, which corresponds to the correct answer option.