Two trains of lengths 105 m and 90 m, respectively run at the speeds of 45km/h and72km/h,respectively in opposite directions on parallel tracks. Find the time which they take to cross each other.

Options

A. a. 5s
B. b. 6s
C. c. 7s
D. d. 8s

Answer

To solve the problem of how long it takes for two trains to cross each other, we can follow these steps:

### Step 1: Understand the Problem
We have two trains:
- Train 1: Length = 105 m, Speed = 45 km/h
- Train 2: Length = 90 m, Speed = 72 km/h

They are moving in opposite directions on parallel tracks.

### Step 2: Convert Speeds from km/h to m/s
To work with the lengths in meters, we need to convert the speeds from kilometers per hour to meters per second. The conversion factor is:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]

For Train 1:
\[ \text{Speed}_1 = 45 \times \frac{5}{18} = \frac{225}{18} = 12.5 \, \text{m/s} \]

For Train 2:
\[ \text{Speed}_2 = 72 \times \frac{5}{18} = \frac{360}{18} = 20 \, \text{m/s} \]

### Step 3: Calculate the Total Length of the Trains
The total length of both trains when they cross each other is:
\[ \text{Total Length} = \text{Length}_1 + \text{Length}_2 = 105 \, \text{m} + 90 \, \text{m} = 195 \, \text{m} \]

### Step 4: Calculate the Relative Speed
Since the trains are moving in opposite directions, we add their speeds to find the relative speed:
\[ \text{Relative Speed} = \text{Speed}_1 + \text{Speed}_2 = 12.5 \, \text{m/s} + 20 \, \text{m/s} = 32.5 \, \text{m/s} \]

### Step 5: Calculate the Time to Cross Each Other
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Total Length}}{\text{Relative Speed}} \]
we can substitute the values we found:
\[ \text{Time} = \frac{195 \, \text{m}}{32.5 \, \text{m/s}} \]

Now, performing the division:
\[ \text{Time} = 6 \, \text{seconds} \]

### Final Answer
The time taken for the two trains to cross each other is **6 seconds**.

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