Question

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?

Answer 1

Here is the solution:

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:

`s= v_(D) * T_(D)`
"D" symbol refers do diesel train

Freight train moves with 15[km/h] greater speed and it travels 1 [h] shorter then:

`s = v_(F) * T_(F) = (v_(D)+15)*(T_(D)-1)`

As the distance made by both train is the same you can compare the right parts of both equations:

`v_(D) * T_(D)=v_(F) * T_(F) = (v_(D)+15)*(T_(D)-1)`

Diesel train moved 6 hours and freight train 5 hours then:

`v_(D) * 6=(v_(D)+15)*5`

`6*v_(D)=5*v_(D)+75`

`6*v_(D)-5*v_(D)=75`

`v_(D)=75`

Here is your answer: The average diesel train speed is 75 km/h