Train P crosses a pole in 30 seconds and the speed of train Q is 54 k...
To find the length of train Q, we need to analyze the given information step by step.
Given Information:
- Train P crosses a pole in 30 seconds.
- The speed of train Q is 54 km/hr more than the speed of train P.
- Train Q crosses train P running in the same direction in 50 seconds.
- Train P crosses a 90m long platform in 36 seconds.
Step 1: Find the speed of train P
Since train P crosses a pole in 30 seconds, we can calculate its speed using the formula: Speed = Distance / Time.
As the pole has no length, the distance covered by train P is 0. Therefore, the speed of train P is also 0.
Step 2: Find the speed of train Q
The speed of train Q is given as 54 km/hr more than the speed of train P. Since the speed of train P is 0, the speed of train Q is 54 km/hr.
Step 3: Find the length of train P
When train Q crosses train P running in the same direction, the time taken is 50 seconds. As train P has no length, the length of train Q is equal to the distance covered by train Q in 50 seconds, which is given by the formula: Distance = Speed × Time.
Therefore, the length of train Q is 54 km/hr × 50 seconds.
Step 4: Find the length of train Q
Now, we need to find the length of train Q using the information that train P crosses a 90m long platform in 36 seconds.
When train P crosses the platform, it covers the distance equal to the length of the train plus the length of the platform. This distance is given by the formula: Distance = Length of Train P + Length of Platform.
Therefore, the length of train P is equal to the distance covered by train P in 36 seconds minus the length of the platform, which is given by the formula: Length of Train P = Distance - Length of Platform.
Step 5: Calculate the length of train Q
Using the information from step 4, the length of train Q can be calculated as follows:
Length of Train Q = Length of Train P + Length of Platform.
Therefore, the correct answer is option B) 300m.
Train P crosses a pole in 30 seconds and the speed of train Q is 54 k...
Length of train P = x
Length of train Q = y
Speed of train P = p
(x + y)/(54 * 5/18) = 50
x + y = 750
x/p = 30
(x + 90)/p = 36
90/p = 6
p = 15 m/s
x = 15 * 30 = 450
y = 750 – 450 = 300m