A man leves from P at 6am and reaches Q at 2 pm on the same day. Another man leaves Q at 8 am and reaches P at 3 pm on the same day. At what time do they meet?

Options

A. `11:46` `"a:m"`
B. `11:24` `"a:m"`
C. `10:48` `"a:m"`
D. `11:00` `"a:m"`

Answer

To solve the problem of when the two men meet, we can follow these steps:

### Step 1: Determine the total distance between P and Q.
Let's assume the distance between P and Q is 56 km.

### Step 2: Calculate the speed of the first man (A).
- Man A leaves P at 6 AM and reaches Q at 2 PM.
- Total time taken by A = 2 PM - 6 AM = 8 hours.
- Speed of A = Distance / Time = 56 km / 8 hours = 7 km/h.

### Step 3: Calculate the speed of the second man (B).
- Man B leaves Q at 8 AM and reaches P at 3 PM.
- Total time taken by B = 3 PM - 8 AM = 7 hours.
- Speed of B = Distance / Time = 56 km / 7 hours = 8 km/h.

### Step 4: Calculate the distance traveled by A before B starts.
- Man A starts at 6 AM and Man B starts at 8 AM, so A travels for 2 hours before B starts.
- Distance traveled by A in 2 hours = Speed of A × Time = 7 km/h × 2 hours = 14 km.

### Step 5: Calculate the remaining distance between A and B when B starts.
- Total distance = 56 km.
- Distance traveled by A before B starts = 14 km.
- Remaining distance = 56 km - 14 km = 42 km.

### Step 6: Calculate the relative speed of A and B.
- Since A is moving towards Q and B is moving towards P, their speeds add up.
- Relative speed = Speed of A + Speed of B = 7 km/h + 8 km/h = 15 km/h.

### Step 7: Calculate the time taken to meet after B starts.
- Time to meet = Remaining distance / Relative speed = 42 km / 15 km/h = 2.8 hours (which is 2 hours and 48 minutes).

### Step 8: Calculate the time they meet.
- B starts at 8 AM, and they take 2 hours and 48 minutes to meet.
- Time of meeting = 8 AM + 2 hours 48 minutes = 10:48 AM.

### Final Answer:
The two men meet at **10:48 AM**.

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