Question

Model train tracks are set up as shown. Each circle is 210 meters. The red and the blue train start at opposite sides of the course. Each train only uses two circles, their whole journey can be described as a number eight. The red train is going clockwise with 20 meters per minute, the blue train counter-clockwise with 15 meters per minute. How long does it take until the trains pass each other?

Answer 1

You never gave the speed of the blue train. The path to collision is equal to 1½ circles. 1.5 x 210 meters = 315 meters I'm going to arbitrarily guess the speed of the blue train is 15 meters per minute. They are therefore approaching each other at a combined rate of 35 meters per minute. 315 / 35 = 9 minutes Answer: 9 minutes

Answer 2

The correct answer is:

9 minutes.

Explanation:

The red train travels clockwise, while the blue train travels counter-clockwise. They will not collide; instead they will be at opposite ends of the center circle at the same time.

This will be after the red train travels half of its circle, half of the center, and another half of the center; this is 1.5 circles.

This is also after the blue train travels half of its circle, half of the center, and another half of the center; this is 1.5 circles.

Each circle is 210 m; this means 1.5 circles is equal to 1.5(210) = 315 m.

The red train travels at 20 m per minute, while the blue train travels at 15 m per minute; this is a combined speed of 20+15 = 35 m per minute.

This means it will take 315/35 = 9 minutes for them to arrive at the point where they pass.