Two trains are going from Bangalore to Chennai with a speed of 80km/hr and 100km/hr. If the train with slower speed starts 1 hour before then find the time taken by the second train to catch the 1st train

Options

A. A)6 hours
B. B)5 hours
C. C)4 hours
D. D)8 hours

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Problem
We have two trains:
- Train A (slower) travels at 80 km/hr.
- Train B (faster) travels at 100 km/hr.
Train A starts its journey 1 hour before Train B.

### Step 2: Calculate the Distance Covered by Train A in 1 Hour
Since Train A starts 1 hour earlier, we can calculate the distance it covers in that hour.
- Distance = Speed × Time
- Distance covered by Train A in 1 hour = 80 km/hr × 1 hr = 80 km

### Step 3: Determine the Relative Speed
When Train B starts, it needs to cover the distance that Train A has already covered (80 km). The relative speed between the two trains is the difference in their speeds.
- Relative Speed = Speed of Train B - Speed of Train A
- Relative Speed = 100 km/hr - 80 km/hr = 20 km/hr

### Step 4: Calculate the Time Taken by Train B to Catch Train A
Now, we can find out how long it will take for Train B to catch up with Train A using the formula:
- Time = Distance / Speed
- Time = 80 km / 20 km/hr = 4 hours

### Step 5: Conclusion
Thus, the time taken by the second train (Train B) to catch the first train (Train A) is 4 hours.

### Final Answer
The time taken by the second train to catch the first train is **4 hours**.

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