A boat travels 18 km towards upstream in 6 hours. How long (In Hrs) will it take to cover the same distance downstream the speed current is one fourth the speed of boat in still water.

Options

A. 3
B. 4
C. 3.6
D. 3.4

Answer

To solve the problem step by step, let's break it down:

1. **Understanding the Problem**:
- A boat travels 18 km upstream in 6 hours.
- The speed of the current is one-fourth of the speed of the boat in still water.
- We need to find out how long it will take to cover the same distance downstream.

2. **Calculate the Speed of the Boat Upstream**:
- Distance = 18 km
- Time = 6 hours
- Speed = Distance / Time
- Speed of the boat upstream = 18 km / 6 hours = 3 km/h

3. **Let the Speed of the Boat in Still Water be 'x'**:
- The speed of the current = (1/4) * x
- The effective speed of the boat upstream = Speed of the boat in still water - Speed of the current
- Therefore, 3 km/h = x - (1/4)x
- Simplifying this gives us:
\[ 3 = \frac{3}{4}x \]

4. **Solve for 'x' (Speed of the Boat in Still Water)**:
- Multiply both sides by 4 to eliminate the fraction:
\[ 12 = 3x \]
- Now divide both sides by 3:
\[ x = 4 \text{ km/h} \]
- So, the speed of the boat in still water is 4 km/h.

5. **Calculate the Speed of the Current**:
- Speed of the current = (1/4) * x = (1/4) * 4 km/h = 1 km/h.

6. **Calculate the Speed of the Boat Downstream**:
- The effective speed of the boat downstream = Speed of the boat in still water + Speed of the current
- Therefore, Speed downstream = 4 km/h + 1 km/h = 5 km/h.

7. **Calculate the Time Taken to Travel Downstream**:
- Time = Distance / Speed
- Time taken to cover 18 km downstream = 18 km / 5 km/h = 3.6 hours.

8. **Final Answer**:
- It will take the boat 3.6 hours to cover the same distance downstream.