Two trains are moving in opposite directions at speeds of 60 km/hour and 90 km/hour. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is

Options

A. 36
B. 49
C. 45
D. 48

Answer

To solve the problem of the two trains moving in opposite directions, we can follow these steps:

### Step 1: Determine the speeds of the trains
The speeds of the two trains are given as:
- Speed of the slower train = 60 km/h
- Speed of the faster train = 90 km/h

### Step 2: Calculate the relative speed
When two objects move in opposite directions, their relative speed is the sum of their speeds. Therefore, we can calculate the relative speed as follows:

\[ \text{Relative Speed} = 60 \, \text{km/h} + 90 \, \text{km/h} = 150 \, \text{km/h} \]

### Step 3: Convert the relative speed to meters per second
To convert the speed from kilometers per hour to meters per second, we use the conversion factor \( \frac{5}{18} \):

\[ \text{Relative Speed in m/s} = 150 \times \frac{5}{18} = \frac{750}{18} = 41.67 \, \text{m/s} \]

### Step 4: Calculate the total distance to be covered
The total distance that the slower train needs to cross the faster train is the sum of their lengths:

- Length of the slower train = 1.10 km = 1100 m
- Length of the faster train = 0.9 km = 900 m

Thus, the total distance is:

\[ \text{Total Distance} = 1100 \, \text{m} + 900 \, \text{m} = 2000 \, \text{m} \]

### Step 5: Use the formula to find the time taken to cross
We can use the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Rearranging this gives us:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values we have:

\[ \text{Time} = \frac{2000 \, \text{m}}{41.67 \, \text{m/s}} \approx 48 \, \text{seconds} \]

### Final Answer
The time taken by the slower train to cross the faster train is approximately **48 seconds**.

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