A person walks from his home to the railway station at a constant speed. If he walks at 4 km/h, he reaches the station 10 minutes late. If he walks at 6 km/h, he reaches the station 5 minutes early. What is the distance between his home and the railway station?

ATQ, Let the distance between home and station be D km. Let the scheduled (exact) time allowed to reach the station be T hours. Case 1: Speed = 4 km/h, reaches 10 minutes late. Time taken = D / 4 hours. So, D / 4 = T + 10 minutes 10 minutes = 10/60 = 1/6 hour ⇒ D / 4 = T + 1/6 … (1) Case 2: Speed = 6 km/h, reaches 5 minutes early. Time taken = D / 6 hours. So, D / 6 = T − 5 minutes 5 minutes = 5/60 = 1/12 hour ⇒ D / 6 = T − 1/12 … (2) Subtract (2) from (1): (D / 4) − (D / 6) = (T + 1/6) − (T − 1/12) Left side: D(1/4 − 1/6) = D[(3 − 2)/12] = D/12 Right side: T + 1/6 − T + 1/12 = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 So, D / 12 = 1/4 ⇒ D = 12 × 1/4 = 3 km