Question

Train A leaves a station 45 minutes before train B. Both trains travel in the same direction and their speeds are 36km/h and 48km/h respectively.

i) How long will it take train B to catch up with train A? ii) How far from the start were the two trains when they met

Answer 1

Train B catches up with train A at 2.25 h

The two trains meet at 108 Km from the start

Explanation:

Relative Speed

There are two trains, A and B leaving the same station. Train A leaves 45 minutes before train B at va=36 Km/h. Train B travels at vb=48 Km/h in the same direction, so they eventually meet.

i)

Calculate the head start of train A Xh, i.e. the distance it traveled in 45 minutes = 45/60=0.75 h.

`X_h=36*0.75=27~Km`

When train A is 27 Km ahead, train B leaves the station. The relative speed between them is vb-ba=48 - 36 = 12 Km/h.

Thus, for train B to meet with train A, the head start must be traveled at the relative speed.

The time needed to do that is:

`\displaystyle t=(27~Km)/(12~Km/h)`

t = 2.25 h

Train B catches up with train A at 2.25 h

ii) In the time calculated above, train B has traveled a distance of:

`X_b=48~Km/h*2.25~h=108~Km`

The two trains meet at 108 Km from the start