# Two trains P and Q, travelling in opposite directions, cross each other in 45 seconds. The speed of train P is 240 km/h, while the speed of train Q is

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Two trains P and Q, travelling in opposite directions, cross each other in 45 seconds. The speed of train P is 240 km/h, while the speed of train Q is 200 m/s. The length of train P is 1500 metres. Find the length of train Q.
1. 15700 m
2. 14500 m
3. 18800 m
4. 10500 m

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Correct Answer - Option 4 : 10500 m

Given

Time = 45 seconds

Speed of train P = 240 km/h

Formula used

Time = [(length of train(1) + length of train(2)]/(speed of first train + speed of second train)

When the objects are moving in opposite directions, then their relative speed is the sum of their speed.

1 km = 1000 /(60 x 60) m/s

Calculation

Speed of train P = [(240 × 1000)/(60 × 60)] = 4000/60

⇒ Speed of train P = 200/3 m/s

45 = (1500 + length of second train)/[(200/3) + 200)]

⇒ 45 = (1500 + length of second train)/[(200 + 600)/3]

⇒ 45 = (1500 + length of second train)/(800/3)

⇒ 45 × 800 = 4500 + 3 length of second train

⇒ 36,000 = 4500 + 3 length of second train

⇒ 31,500 = 3 length of second train

⇒ 10,500 = length of second train

∴ Length of second train is 10,500 m