A train completely overtakes two persons, walking in the same direction with speeds 3 km/hr and 4 km/hr in 9 seconds and 75/8 seconds respectively. What is the length of the train?

Let speed of train = v km/hr, length = L m. L = (v−3)·9·(1000/3600) = (v−3)·9/3.6 = 2.5(v−3). Also L = (v−4)·(75/8)/3.6. Equate: 2.5(v−3) = (75/8)(v−4)/3.6 = 75(v−4)/(8·3.6) = 75(v−4)/28.8. 2.5·28.8(v−3) = 75(v−4) ⟹ 72(v−3) = 75(v−4) ⟹ 72v−216 = 75v−300 ⟹ 3v = 84 ⟹ v = 28. L = 2.5·25 = 62.5 m.