2023 · Q78
A train completely overtakes two persons, walking in the same direction with speeds 3 km/h and 4 km/h in 9 seconds and 75/8 seconds respectively. What is the length of the train?
Elementary MathematicsTime, Speed and Distance
- A60 m
- B62.5 m
- C55 m
- D67.5 m
Explanation
Let the train's speed be v km/h and its length L metres. Overtaking the 3 km/h walker takes 9 s with relative speed (v−3) km/h, so L = (v−3)·9/3600 km; overtaking the 4 km/h walker takes 75/8 = 9.375 s, so L = (v−4)·9.375/3600 km. Equating: 9(v−3) = 9.375(v−4), giving 9v − 27 = 9.375v − 37.5, so 0.375v = 10.5 and v = 28 km/h. Then L = (28−3)·9/3600 km = 225/3600 km = 62.5 m. The answer is (B).