The distance between two stations P and Q is 145 km. A train with speed of 25 km/h leaves station at 8:00 am towards station Q. Another train with speed of 35km/h leaves station Q at 9:00 am towards station P.Then, at what time both trains meet?

Options

A. a. `12:00 am`
B. b. `11:30 am`
C. c. `12:00 am`
D. d. `11:30 am`

Answer

To solve the problem step by step, we need to determine when the two trains meet. Here’s how we can do that:

### Step 1: Understand the problem
We have two trains:
- Train A leaves station P at 8:00 AM with a speed of 25 km/h.
- Train B leaves station Q at 9:00 AM with a speed of 35 km/h.
The distance between the two stations P and Q is 145 km.

### Step 2: Calculate the distance covered by Train A before Train B starts
Train A travels for 1 hour before Train B starts.
- Distance covered by Train A in 1 hour = Speed × Time = 25 km/h × 1 h = 25 km.

### Step 3: Calculate the remaining distance between the two trains when Train B starts
- Remaining distance = Total distance - Distance covered by Train A = 145 km - 25 km = 120 km.

### Step 4: Calculate the relative speed of the two trains
Since both trains are moving towards each other, we can add their speeds to find the relative speed.
- Relative speed = Speed of Train A + Speed of Train B = 25 km/h + 35 km/h = 60 km/h.

### Step 5: Calculate the time taken for the trains to meet
Using the formula: Time = Distance / Speed,
- Time taken to meet = Remaining distance / Relative speed = 120 km / 60 km/h = 2 hours.

### Step 6: Determine the meeting time
Train B starts at 9:00 AM, and it takes 2 hours for the trains to meet.
- Meeting time = 9:00 AM + 2 hours = 11:00 AM.

### Final Answer
Both trains will meet at **11:00 AM**.

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