A passenger train that runs at the speed of 78 km/h leaves the station 8 hours after the goods train left and overtakes it in 5 hours. What is the speed of goods train?

Let goods train speed = x km/h. Goods train travels for 8 + 5 = 13 hours before being overtaken. Passenger train speed = 78 km/h travels for 5 hours. Distance is same: 13x = 78 × 5 = 390. So x = 390 / 13 = 30 km/h. The key insight is that the goods train had an 8-hour head start, then both trains traveled for 5 more hours before the passenger train caught up.