Directions: Use the information below to answer the question.

Train P passes a signal post in 15 seconds and clears a 200-metre platform in 25 seconds. How long will Train P take to pass Train Q, which is 420 metres long and travels at 90 km/hr in the opposite direction?

The correct answer is 16 seconds.

Step 1: Find the speed and length of Train P.

When a train passes a signal post, the distance covered is equal to the length of the train itself. Let the length of Train P be $L_P$ metres and its speed be $v_P$ m/s.

When Train P clears a 200-metre platform, the total distance covered is the sum of the length of the train and the platform length, which takes 25 seconds:

Subtracting the first equation from the second equation:

Now, calculate the length of Train P:

Step 2: Convert the speed of Train Q to metres per second (m/s).

The speed of Train Q is given as 90 km/hr. To convert km/hr to m/s, multiply by $\frac{5}{18}$:

Step 3: Calculate the relative speed and total distance to cross each other.

Since the two trains are travelling in opposite directions, their relative speed is the sum of their individual speeds:

The total distance to be covered when passing each other is the sum of the lengths of both trains:

Step 4: Calculate the time taken to pass Train Q.

Using the formula $\text{Time}=\frac{\text{Total Distance}}{\text{Relative Speed}}$:

Thus, Train P will take 16 seconds to pass Train Q.