A metro train A starts from Kahsmere Gate at 6:00 AM to reach Iffco Chowk at 7:00 AM while another train B starts from Iffco Chowk at 6:20 AM to reach Kashmere Gate at 7:00 AM. At what time both trains will meet each other if distance between stations is 24 km.

Options

A. A)`6:32` AM
B. B)`6:36` AM
C. C)`6:40` AM
D. D)`6:28` AM

Answer

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

### Step 1: Determine the speed of Train A
Train A starts from Kashmere Gate at 6:00 AM and reaches Iffco Chowk at 7:00 AM. The distance between the two stations is 24 km.

- **Speed of Train A** = Distance / Time
- **Time taken by Train A** = 1 hour (from 6:00 AM to 7:00 AM)
- **Speed of Train A** = 24 km / 1 hour = 24 km/h

**Hint:** Remember that speed is calculated by dividing distance by time.

### Step 2: Determine the speed of Train B
Train B starts from Iffco Chowk at 6:20 AM and reaches Kashmere Gate at 7:00 AM.

- **Time taken by Train B** = 40 minutes (from 6:20 AM to 7:00 AM)
- Convert 40 minutes to hours: 40 minutes = 40/60 hours = 2/3 hours.
- **Speed of Train B** = Distance / Time = 24 km / (2/3) hours = 24 km * (3/2) = 36 km/h

**Hint:** When calculating speed, ensure to convert minutes into hours for consistency.

### Step 3: Calculate the distance covered by Train A before Train B starts
Train B starts at 6:20 AM, while Train A has already been traveling since 6:00 AM.

- **Time difference** = 20 minutes = 1/3 hours.
- **Distance covered by Train A in 20 minutes** = Speed × Time = 24 km/h × (1/3) hours = 8 km.

**Hint:** Calculate the distance covered by a train using its speed and the time it has been traveling.

### Step 4: Determine the remaining distance when Train B starts
When Train B starts at 6:20 AM, Train A has already covered 8 km.

- **Remaining distance** = Total distance - Distance covered by Train A = 24 km - 8 km = 16 km.

**Hint:** Always subtract the distance already covered from the total distance to find the remaining distance.

### Step 5: Calculate the relative speed of both trains
Both trains are moving towards each other, so we can add their speeds to find the relative speed.

- **Relative speed** = Speed of Train A + Speed of Train B = 24 km/h + 36 km/h = 60 km/h.

**Hint:** When two objects move towards each other, their speeds add up.

### Step 6: Calculate the time taken to meet
Now, we can find the time taken for both trains to meet using the remaining distance and their relative speed.

- **Time to meet** = Remaining distance / Relative speed = 16 km / 60 km/h = 16/60 hours = 4/15 hours.

**Hint:** Time can be calculated by dividing distance by speed.

### Step 7: Convert time into minutes and find the meeting time
4/15 hours can be converted into minutes:

- **Time in minutes** = (4/15) × 60 minutes = 16 minutes.

Since Train B starts at 6:20 AM, we add 16 minutes to this time:

- **Meeting time** = 6:20 AM + 16 minutes = 6:36 AM.

**Hint:** Always convert hours into minutes for easier addition when calculating time.

### Final Answer
Both trains will meet each other at **6:36 AM**.