Two trains are moving in opposite directions with the same speed. If the length of each train is 144 metres and they cross each other in 9 seconds, then what is the speed (in km/hr) of each train?

Options

A. 53
B. `57.6`
C. `60.4`
D. `64.8`

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Problem
We have two trains moving in opposite directions, each with a length of 144 meters. They cross each other in 9 seconds. We need to find the speed of each train in km/hr.

### Step 2: Calculate the Total Distance
When two trains cross each other, the total distance covered is the sum of their lengths. Therefore, the total distance \( D \) is:
\[ D = 144 \, \text{meters} + 144 \, \text{meters} = 288 \, \text{meters} \]

### Step 3: Determine the Time Taken
The time taken \( T \) to cross each other is given as 9 seconds.

### Step 4: Use the Speed Formula
The speed \( S \) is given by the formula:
\[ S = \frac{D}{T} \]
Substituting the values we have:
\[ S = \frac{288 \, \text{meters}}{9 \, \text{seconds}} = 32 \, \text{meters/second} \]

### Step 5: Convert Speed to km/hr
To convert the speed from meters per second to kilometers per hour, we use the conversion factor \( \frac{18}{5} \):
\[ S_{km/hr} = S_{m/s} \times \frac{18}{5} \]
Substituting the speed:
\[ S_{km/hr} = 32 \times \frac{18}{5} = \frac{576}{5} = 115.2 \, \text{km/hr} \]

### Step 6: Calculate the Speed of Each Train
Since both trains are moving at the same speed and they are moving in opposite directions, the speed of each train \( x \) is half of the total speed:
\[ x = \frac{115.2}{2} = 57.6 \, \text{km/hr} \]

### Final Answer
The speed of each train is **57.6 km/hr**.

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