72km/h = (72 × 1000)m/h = 72000m/h
So since 1 hour = 60 min = 60 × 60 seconds = 3600 seconds,
Speed of passenger train = (72000m ÷ 3600)/s = 20m/s
For the goods train, speed = 54km/h = (54 × 1000m ÷ 3600)/s = 15m/s
Now it takes 8 seconds for the passenger train to pass the goods train. This might be confusing since both trains are moving.
But what is important is that : passenger train travels past the goods train by 20m in 1 second.
So in 8 seconds, the passenger train travels past the goods train by 8 × 20m = 160m. Its front is now 160m ahead of the goods train's front. Its rear is also 160m ahead as compared to before. There is still some distance left to pass the goods train completely.
Now that was assuming that the goods train was stationary. It is not stationary, however.
In the same 8 seconds, it passes by the passenger train by 8 × 15m = 120m. The rear of the goods train is now 120m ahead of its original position, and has just passed the rear of the passenger train. So this tells us that the distance of 120m is basically that 'distance left to pass the train completely' , if the goods train were stationary.
Length of goods train = 160m + 120m = 280m
(If it gets confusing, move one train first on paper, mark the position. Then move the other and mark the position. You'll see that the length of the slower train is the combined distance the two trains travelled in that same 8 seconds)