A 360m-long train takes 4.5 seconds to cross a pole. The same train takes 6 seconds to cross a car moving in the same direction. What is the speed (in `km//hr`) of the car? (Assume the length of the car to be negligible.)

Options

A. 60
B. 72
C. 84
D. 96

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the speed of the train.
The speed of the train can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Given that the length of the train is 360 meters and it takes 4.5 seconds to cross a pole, we can substitute the values into the formula:
\[ \text{Speed of the train} = \frac{360 \text{ m}}{4.5 \text{ s}} \]

### Step 2: Simplify the calculation.
To simplify the calculation, we can convert 4.5 seconds into a fraction:
\[ 4.5 = \frac{45}{10} = \frac{9}{2} \]
Now, substituting back into the speed formula:
\[ \text{Speed of the train} = \frac{360}{\frac{9}{2}} = 360 \times \frac{2}{9} = 80 \text{ m/s} \]

### Step 3: Use the speed of the train to find the speed of the car.
The train takes 6 seconds to cross the car. Since the car is moving in the same direction, we can use the relative speed concept. The relative speed of the train with respect to the car is:
\[ \text{Relative Speed} = \text{Speed of the train} - \text{Speed of the car} \]
Using the time taken to cross the car:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
The distance the train covers while crossing the car is equal to the length of the train (360 meters):
\[ 360 = (80 - v) \times 6 \]
Where \( v \) is the speed of the car in m/s.

### Step 4: Solve for the speed of the car.
Rearranging the equation:
\[ 360 = 480 - 6v \]
\[ 6v = 480 - 360 \]
\[ 6v = 120 \]
\[ v = \frac{120}{6} = 20 \text{ m/s} \]

### Step 5: Convert the speed of the car to km/hr.
To convert from m/s to km/hr, we multiply by 18/5:
\[ \text{Speed of the car in km/hr} = 20 \times \frac{18}{5} = 72 \text{ km/hr} \]

### Final Answer:
The speed of the car is **72 km/hr**.

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