Two trains approach each other at 30 km/hr and 27 km/hr from two places 342 km apart. After how many hours do they meet?

Options

A. 5 hours
B. 6 hours
C. ` 1 (2)/(3) `hours
D. ` 2 (2)/(3)` hours

Answer

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

### Step 1: Determine the speeds of the trains
- Train A is traveling at a speed of 30 km/hr.
- Train B is traveling at a speed of 27 km/hr.

### Step 2: Calculate the combined speed of the two trains
- The combined speed of both trains when they are moving towards each other is the sum of their speeds:
\[ \text{Combined Speed} = 30 \text{ km/hr} + 27 \text{ km/hr} = 57 \text{ km/hr} \]

### Step 3: Identify the distance between the two trains
- The distance between the two trains is given as 342 km.

### Step 4: Use the formula to find the time taken to meet
- The formula to calculate time when distance and speed are known is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Plugging in the values:
\[ \text{Time} = \frac{342 \text{ km}}{57 \text{ km/hr}} \]

### Step 5: Perform the division
- Now, we will calculate the time:
\[ \text{Time} = 6 \text{ hours} \]

### Conclusion
- Therefore, the two trains will meet after **6 hours**.

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