A train with 90 km/h crosses a bridge in 36 seconds. Another train 100 metres…
2023
A train with 90 km/h crosses a bridge in 36 seconds. Another train 100 metres shorter crosses the same bridge at 45 km/h. What is the time taken by the second train to cross the bridge?
- A.
72 seconds
- B.
64 seconds
- C.
60 seconds
- D.
68 seconds
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Answer: 64 seconds
Convert speeds to metres per second: 90 km/h = 90 × (5/18) = 25 m/s; 45 km/h = 45 × (5/18) = 25/2 m/s.
Let the longer train length be x metres and the bridge length be y metres. Time for the longer train to cross the bridge = (x + y) / 25 = 36 s, so x + y = 25 × 36 = 900 m.
The shorter train is 100 m shorter, so its length is x − 100. Its distance to clear the bridge = (x − 100) + y = (x + y) − 100 = 900 − 100 = 800 m.
Time for the shorter train = distance / speed = 800 ÷ (25/2) = 800 × 2 / 25 = 1600 / 25 = 64 s.
Therefore, the time taken by the second train to cross the bridge is 64 seconds.