The distance between AB is 174 km. Two boats start moving towards each other at the same time at point A & B respectively. One in upstream and other in downstream. If their speed in still water is 9.6 km/hr. and 19.4 km/hr. respectively. Then in how much time they will meet.

Options

A. 9 hr.
B. 7 hr.
C. 4.5 hr.
D. 6 hr.

Answer

To solve the problem, we need to determine how long it will take for the two boats to meet when they start moving towards each other from points A and B.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Distance between A and B = 174 km
- Speed of Boat A (upstream) = 9.6 km/hr
- Speed of Boat B (downstream) = 19.4 km/hr

2. **Calculate the Relative Speed:**
- Since the boats are moving towards each other, we can add their speeds to find the relative speed.
- Relative Speed = Speed of Boat A + Speed of Boat B
- Relative Speed = 9.6 km/hr + 19.4 km/hr = 29 km/hr

3. **Use the Formula for Time:**
- The formula to calculate time when distance and speed are known is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Here, the distance is 174 km and the relative speed is 29 km/hr.

4. **Calculate the Time Taken to Meet:**
- Time = \(\frac{174 \text{ km}}{29 \text{ km/hr}}\)
- Time = 6 hours

### Final Answer:
The two boats will meet after **6 hours**.

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