he lengths of train P and train Q are 270 m and 330 m respectively. The average speed of trains P and Q is equal to the difference between the speeds of trains P and Q which is equal to 108 km/hr. If train Q crosses train P running in the same direction in 'a + 5' seconds then find the length of the platform that train P crosses in 'a + 35' seconds

Let's break down the information given step by step:

1. The length of train P is 270 m and the length of train Q is 330 m.
2. The average speed of trains P and Q is equal to the difference between their speeds, which is 108 km/hr.
3. Train Q crosses train P running in the same direction in 'a + 5' seconds.

To find the length of the platform that train P crosses in 'a + 35' seconds, we need to use the concept of relative speed.

Relative speed is the difference in speeds between two objects moving in the same direction. In this case, the relative speed between train P and train Q is 108 km/hr.

Now, let's calculate the time it takes for train Q to cross train P:

Relative speed = 108 km/hr = (108 * 1000) / 3600 m/s = 30 m/s

Distance = Length of train P = 270 m

Time = Distance / Relative speed = 270 / 30 = 9 seconds

Given that train Q crosses train P in 'a + 5' seconds, we can write the equation:

a + 5 = 9

Solving this equation, we find:

a = 4

Now, let's calculate the length of the platform that train P crosses in 'a + 35' seconds:

Time = a + 35 = 4 + 35 = 39 seconds

Since the platform length is the distance covered by train P in this time, we can use the formula:

Distance = Speed * Time

The speed of train P is the average speed of both trains, which is 108 km/hr. Converting it to m/s:

Speed = 108 km/hr = (108 * 1000) / 3600 m/s = 30 m/s

Distance = Speed * Time = 30 * 39 = 1170 m

Therefore, the length of the platform that train P crosses in 'a + 35' seconds is 1170 m.