A 234 m long train passes a person running at 9 km/h in the opposite direction, in 6 seconds. In how much time (in seconds) will it pass another person who is moving at 23.4 km/h, in the same direction?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 7.8.
Distance = Speed × Time
When two objects are moving in opposite direction, the relative speed of the two objects is equal to the sum of the individual speeds of the objects.
Also, When two objects are moving in same direction, the relative speed of the two objects is equal to the difference of the individual speeds of the objects.
Let the speed of the train be x km/h.
According to the given question,
Relative speed of train and the first person = (x + 9) km/h
Relative speed of train and the first person in m/sec = (x + 9) × m/sec
Now, (x + 9) × × 6 = 234
⇒ x + 9 = 48 × 3
⇒ x + 9 = 140.4
⇒ x = 131.4 km/h
Now, relative speed of train and the second person = (131.4 - 23.4) km/h = 108 km/h
Relative speed of train and the second person in m/sec = 108 × m/sec = 30 m/sec
Time taken = = 7.8 sec
Hence the train will pass the second person in 7.8 seconds.