Two trains along the same straight rails moving the constant speed `60km//hr` and `30km//hr` respectively towards each other. If at time `t=0`, the distance between then is `90km`, the time when they collide is

Options

A. 1 hr
B. 2 hr
C. 3 hr
D. 4 hr

Answer

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

### Step 1: Identify the speeds of the trains
- Train 1 is moving at a speed of \(60 \, \text{km/h}\).
- Train 2 is moving at a speed of \(30 \, \text{km/h}\).

### Step 2: Determine the initial distance between the trains
- The initial distance between the two trains is \(90 \, \text{km}\).

### Step 3: Calculate the relative speed of the trains
Since the trains are moving towards each other, we can add their speeds to find the relative speed:
\[ \text{Relative Speed} = \text{Speed of Train 1} + \text{Speed of Train 2} = 60 \, \text{km/h} + 30 \, \text{km/h} = 90 \, \text{km/h} \]

### Step 4: Use the formula for time
To find the time until they collide, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]
Substituting the known values:
\[ \text{Time} = \frac{90 \, \text{km}}{90 \, \text{km/h}} = 1 \, \text{hour} \]

### Conclusion
The two trains will collide after \(1\) hour.

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