A train from A leaves at 7 am at the speed of 70 km/ h to reach B and similarly. A train from B leaves at the speed of 60 km/h at 8 am. If distance between A and B is 720 km. Find the time taken by them to meet each other.

Answer

To solve the problem, we need to determine the time taken by two trains to meet each other, given their speeds and the distance between them. Here’s a step-by-step solution:

### Step 1: Understand the situation
- Train A leaves from point A at 7 AM traveling at a speed of 70 km/h.
- Train B leaves from point B at 8 AM traveling at a speed of 60 km/h.
- The distance between A and B is 720 km.

**Hint:** Identify the departure times and speeds of both trains.

### Step 2: Calculate the distance covered by Train A before Train B starts
Since Train A leaves at 7 AM and Train B leaves at 8 AM, Train A has a 1-hour head start.

- Distance covered by Train A in 1 hour = Speed × Time = 70 km/h × 1 h = 70 km.

**Hint:** Use the formula for distance (Distance = Speed × Time) to find how far Train A travels in the head start.

### Step 3: Calculate the remaining distance between the trains when Train B starts
- Total distance = 720 km.
- Distance covered by Train A in the first hour = 70 km.
- Remaining distance = Total distance - Distance covered by Train A = 720 km - 70 km = 650 km.

**Hint:** Subtract the distance covered by Train A from the total distance to find the distance left when Train B starts.

### Step 4: Calculate the relative speed of both trains
Since both trains are moving towards each other, we can add their speeds to find the relative speed.

- Speed of Train A = 70 km/h.
- Speed of Train B = 60 km/h.
- Relative speed = Speed of Train A + Speed of Train B = 70 km/h + 60 km/h = 130 km/h.

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

### Step 5: Calculate the time taken to meet
Now, we can use the formula for time (Time = Distance / Speed) to find out how long it will take for the two trains to meet.

- Distance to be covered = 650 km.
- Relative speed = 130 km/h.
- Time taken to meet = Distance / Relative speed = 650 km / 130 km/h = 5 hours.

**Hint:** Use the formula for time to find out how long it will take to cover the remaining distance at the relative speed.

### Conclusion
The two trains will meet each other after 5 hours from the time Train B starts, which is at 8 AM. Therefore, they will meet at 1 PM.

**Final Answer:** The time taken by them to meet each other is 5 hours.