Math CentralQuandaries & Queries


Question from Taylor, a student:

Cory and Melissa are racing electronic cars around a circular track. They begin at the same time going in the same diretion. Cory's car completes a revolution in 35 secs, while Melissa's car completes a revolultion in 30 secs. How long will it take them before both cars reach the starting point again simultaneously?

Hi Taylor.

Each 35 seconds, Cory's car passes the starting point, so the answer to the question is a multiple of 35 seconds.

Each 30 seconds, Melissa's car passes the starting point, so the answer is also a multiple of 30 seconds.

What is the lowest common multiple of 35 and 30? That is, what is the smallest number that 35 and 30 both go into evenly?

Hope this helps,
Stephen La Rocque.


Hi Taylor,

My solution to your problem is different that Steve's solution. I like his better than mine but I thought I would show you mine anyway so here goes.

After Corry has made one circuit of the track and Melissa is 5 minutes ahead of him.

After Corry has made two circuits of the track and Melissa is 10 minutes ahead of him.

When Melissa is 30 minutes ahead of Cory she and Cory are both at the starting point. How many circuits has Cory completed when Melissa is 30 minutes ahead? How much time did it take.


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