The distance between two cities A and B is 330 km . A train starts from A at 8 a.m. travels towards B at 60km/hr .
Another train starts from B at 9 a.m. and travels towards A at 75 km/hr . At what time do they meet ?

Options

A. `10:30` am
B. `10:45` am
C. `11` am
D. `11:25` am

Explanation

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

### Step 1: Determine the distance covered by the first train before the second train starts.
- The first train starts from city A at 8 a.m. and travels at a speed of 60 km/hr.
- By 9 a.m., it has been traveling for 1 hour.
- Distance covered by the first train in 1 hour = Speed × Time = 60 km/hr × 1 hr = 60 km.

### Step 2: Calculate the remaining distance between the two trains when the second train starts.
- The total distance between A and B is 330 km.
- Distance remaining when the second train starts = Total distance - Distance covered by the first train = 330 km - 60 km = 270 km.

### Step 3: Determine the speeds of both trains.
- Speed of the first train = 60 km/hr (from A to B).
- Speed of the second train = 75 km/hr (from B to A).

### Step 4: Calculate the relative speed of the two trains.
- When two objects are moving towards each other, their relative speed is the sum of their speeds.
- Relative speed = Speed of first train + Speed of second train = 60 km/hr + 75 km/hr = 135 km/hr.

### Step 5: Calculate the time taken for the two trains to meet.
- Time = Distance / Speed.
- Distance to cover = 270 km (from Step 2).
- Speed = 135 km/hr (from Step 4).
- Time taken to meet = 270 km / 135 km/hr = 2 hours.

### Step 6: Determine the meeting time.
- The second train starts at 9 a.m. and takes 2 hours to meet the first train.
- Meeting time = 9 a.m. + 2 hours = 11 a.m.

### Final Answer:
The two trains will meet at **11 a.m.**.

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