The Train Set Problem

My daughter's birthday present

My daughter’s birthday present

My daughter got a new train set for her birthday. Today we opened it up and put it together. As we got to playing with it, it seemed that the two loops were becoming a focus. We had two trains on the tracks at the same time and every so often, there would be  bit of a collision at the short stretch where the two loops intersect.

Now, that got me thinking. I thought of two questions. Both relating to comparative speed.

1. How much faster would one train have to be for the trains to complete the loops in the same amount of time?

2. If the trains started at the same spot and traveled the same speed, when would they both be at the same spot again?

There are mountains of math problems we could do with this train set. It would be okay with me if you filled the comments with possibilities beyond my two.

An overhead shot, if you think it will help.

An overhead shot, if you think it will help.

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