This is a Grade 9 problem solving question that I need assistance and how to get the answer:

One car leaves a spot traveling at 100 km per hour. The second car leaves the same spot 15 minutes later and traveling at 120 km per hour. How long does it take for the second car to catch up to the first car? Please show how you arrive at the answer.

Student: Jason

Hi Jason,

Have you been on a moving sidewalk, or they are sometimes called people movers. You find them at many airports. It is a large belt of plastic or rubber at the floor level, about a wide as a sidewalk and about half a block long. The belt moves slowly and if you stand on it you move the half a block with no effort on your part.

Imagine that there is a very long moving sidewalk that moves at 100 km/hr. Someone gets on it and then you get on 15 minutes later. The person ahead of you has progressed at 100 km/hr for 1/4 of an hour and hence he is 25 km ahead of you. If both of you stand still you remain 25 km apart even though you are both moving at 100 km/hr. Now you start to walk at 20 km/hr. At this speed it takes you one and a quarter hours to move the 25 km that separate you.

From your point of view, on the moving sidewalk, you traveled at 20 km/hr for an hour and a half to catch the other person. From the point of view of someone not on the moving sidewalk, the first person traveled at 100 km/hr, you traveled at 120 km/hr, and it took you one and a quarter hours to catch up.

I hope this helps,
Penny