The length of a train is one-third of the length of platform A, and the speed of the train is 90 km/hr. If the train can cross platforms A and B in 8 and 12 seconds, then find the length of platform B?
Answer (2)
The length of platform B is calculated to be 250 meters, after establishing the relationships between the lengths of the train and platforms A and B. We found that the length of the train is 50 meters and the length of platform A is 150 meters. Using the crossing times, all calculations lead to the final result for platform B.
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To solve this problem, you need to find the length of platform B based on the given information about a train and two platforms.
Let's define the variables:
Let the length of the train be L t .
Let the length of platform A be 3 L t (since the length of the train is one-third of platform A).
Let the length of platform B be L b .
Given that the speed of the train is 90 km/hr, we first need to convert this speed to meters per second for easier calculation with the time given in seconds:
90 km/hr = 3600 90 × 1000 = 25 m/s
Using the formula:
Distance = Speed × Time
For the train to cross platform A in 8 seconds, the train covers its own length and the length of platform A:
L t + 3 L t = 25 × 8
4 L t = 200
L t = 50 meters
The length of platform A is:
3 L t = 150 meters
For the train to cross platform B in 12 seconds, the train covers its own length and the length of platform B:
L t + L b = 25 × 12
50 + L b = 300
L b = 250 meters
So, the length of platform B is 250 meters.
