7 hours after a goods train passed a station, another train travelling at a speed of 54 km./hr. following that goods train passed through that station. If after passing the station the train overtakes the goods train in 11 hours, what is the speed of the goods train?

Let the speed of goods train be x kmph. ∴ Relative speed of train = (54 – x) kmph. According to the question, Distance covered by goods train in 7 hours = Distance covered by train in 11 hours with relative speed. $Rightarrow 7 x=(54-x) 11$ $Rightarrow 7 x+11 x=54 imes 11$ $Rightarrow 18 x=54 imes 11$ $Rightarrow x=frac{54 imes 11}{18}=33 mathrm{kmph} .$ Alternative: