Two trains, of same length, are running on parallel tracks in the same direction with speed 60 km/hour and 90 km/hour respectively. The latter completely crosses the former in 30 seconds. The length of each train (in metres) is

Options

A. A)125
B. B)150
C. C)100
D. D)115

Answer

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

### Step 1: Determine the speeds of the trains
The speeds of the two trains are given as:
- Speed of Train 1 (T1) = 60 km/hour
- Speed of Train 2 (T2) = 90 km/hour

### Step 2: Calculate the relative speed
Since both trains are moving in the same direction, we need to find the relative speed by subtracting the speed of Train 1 from the speed of Train 2:
\[ \text{Relative Speed} = T2 - T1 = 90 \, \text{km/hour} - 60 \, \text{km/hour} = 30 \, \text{km/hour} \]

### Step 3: Convert the relative speed to meters per second
To convert the speed from km/hour to meters per second, we use the conversion factor \( \frac{5}{18} \):
\[ \text{Relative Speed in m/s} = 30 \times \frac{5}{18} = \frac{150}{18} = \frac{25}{3} \, \text{m/s} \]

### Step 4: Use the time taken to cross each other
The time taken for Train 2 to completely cross Train 1 is given as 30 seconds.

### Step 5: Calculate the distance covered during the crossing
The distance covered when Train 2 crosses Train 1 is equal to the sum of the lengths of both trains, which we denote as \( 2L \) (since both trains are of equal length \( L \)):
\[ \text{Distance} = \text{Relative Speed} \times \text{Time} \]
Substituting the known values:
\[ 2L = \left(\frac{25}{3} \, \text{m/s}\right) \times 30 \, \text{s} \]

### Step 6: Solve for \( 2L \)
Calculating the right side:
\[ 2L = \frac{25 \times 30}{3} = \frac{750}{3} = 250 \, \text{meters} \]

### Step 7: Find the length of each train
Since \( 2L = 250 \, \text{meters} \), we can find \( L \) by dividing by 2:
\[ L = \frac{250}{2} = 125 \, \text{meters} \]

### Final Answer
The length of each train is \( 125 \, \text{meters} \).

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