A pair of commuter trains are travelling along parallel tracks in the same direction. A passenger sitting in the slower train notices that the faster train takes 30 seconds to pass completely by their window. If the speed of the faster train is 18 km/h greater than that of the slower train, what is the length of the faster train in meters?

Correct Answer: The length of the faster train is 150 meters (Option: 150).

Step-by-Step Explanation:

1. Understand Relative Speed:
When two objects move in the same direction, their relative speed is the difference between their individual speeds.
Let the speed of the slower train be $$_slower and the speed of the faster train be $$_faster.

Given that the speed of the faster train is 18 km/h greater than the slower train:

$\text{Relative Speed}=V_{\text{faster}}-V_{\text{slower}}=18\text{km/h}$

2. Convert Relative Speed to Meters per Second (m/s):
To convert speed from km/h to m/s, multiply by $\frac{5}{18}$.

$\text{Relative Speed in m/s}=18\times \frac{5}{18}=5\text{m/s}$

3. Calculate the Length of the Faster Train:
From the perspective of a passenger sitting at a single fixed window in the slower train, the passenger acts as a point object. The time taken for the faster train to pass this window completely is the time required for the faster train to cover its own length at the relative speed.

$\text{Distance (Length of Faster Train)}=\text{Relative Speed}\times \text{Time}$

Given time = 30 seconds:

$\text{Length}=5\text{m/s}\times 30\text{s}=150\text{meters}$

Thus, the length of the faster train is 150 meters.