A train X running at 72km/h crosses another train Y running at 54km/h in opposite direction in 15 seconds. If the length of Y is two-fifth that of X, then what is the length (in meter) of X?
- A375
- B150
- C300
- D225
Solution & Step-by-step Explanation
Let the length of train X be L meters.
According to the question, length of train Y =
5
2
L.
Since they are running in opposite directions, their relative speed is the sum of their speeds:
Relative Speed=72km/h+54km/h=126km/h
Convert relative speed into meters per second (m/s):
Relative Speed=126×
18
5
=7×5=35m/s
The total distance covered when crossing each other is the sum of their lengths:
Total Distance=L+
5
2
L=
5
7
L
Using the formula Distance=Speed×Time:
5
7
L=35×15
5
7
L=525
7L=525×5
L=75×5=375meters
According to the question, length of train Y =
5
2
L.
Since they are running in opposite directions, their relative speed is the sum of their speeds:
Relative Speed=72km/h+54km/h=126km/h
Convert relative speed into meters per second (m/s):
Relative Speed=126×
18
5
=7×5=35m/s
The total distance covered when crossing each other is the sum of their lengths:
Total Distance=L+
5
2
L=
5
7
L
Using the formula Distance=Speed×Time:
5
7
L=35×15
5
7
L=525
7L=525×5
L=75×5=375meters