The distance between two cities A and B is 330 km. A tain starts from A at 8 a.m. and travels towards B at 60 km/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. `10am`
B. `10.30am`
C. `11am`
D. `11.30am`

Answer

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

### Step 1: Determine the distance covered by the first train before the second train starts.
The first train leaves city A at 8 a.m. and travels towards city B at a speed of 60 km/h. The second train leaves city B at 9 a.m.

From 8 a.m. to 9 a.m., the first train travels for 1 hour:
- Distance covered by the first train = Speed × Time = 60 km/h × 1 h = 60 km.

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

### Step 3: Determine the speeds of both trains and their relative speed.
The first train continues at 60 km/h, and the second train starts at 9 a.m. and travels towards A at 75 km/h. The relative speed of the two trains (since they are moving towards each other) is:
- Relative speed = Speed of first train + Speed of second train = 60 km/h + 75 km/h = 135 km/h.

### Step 4: Calculate the time taken for the two trains to meet after the second train starts.
Using the remaining distance of 270 km and the relative speed of 135 km/h, we can find the time taken for the trains to meet:
- Time = Distance / Speed = 270 km / 135 km/h = 2 hours.

### Step 5: Determine the meeting time.
The second train starts at 9 a.m., and it takes 2 hours for the trains to meet. Therefore, they will meet at:
- Meeting time = Start time of the second train + Time taken to meet = 9 a.m. + 2 hours = 11 a.m.

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

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