A diesel train left Abuja and traveled toward Johannesburg. A freight train left one hour later traveling 15 km/h faster in an effort to catch up it. After five hours the freight train finally caught up. What was the diesel train's average speed?
Start with the fact that both trains have made the same distance= 's'.
In physics distance is a multiplication of speed of your train = 'v' and period of time in which it was moving= 'T' (this is only true when the speed doesn't change during movement, or we talk about avarage speed like in your task). Then: [tex]s= v_{D} * T_{D}[/tex] "D" symbol refers do diesel train
Freight train moves with 15[km/h] greater speed and it travels 1 [h] shorter then: [tex]s = v_{F} * T_{F} = (v_{D}+15)*(T_{D}-1)[/tex]
As the distance made by both train is the same you can compare the right parts of both equations: [tex]v_{D} * T_{D}=v_{F} * T_{F} = (v_{D}+15)*(T_{D}-1)[/tex]
Diesel train moved 6 hours and freight train 5 hours then: [tex]v_{D} * 6=(v_{D}+15)*5[/tex] [tex]6*v_{D}=5*v_{D}+75[/tex] [tex]6*v_{D}-5*v_{D}=75[/tex] [tex]v_{D}=75[/tex]
Here is your answer: The average diesel train speed is 75 km/h
