Caleb and Eva are running around a track. They both start at the same time. It takes Caleb 18 minutes to complete 1 lab. It takes Eva 14 minutes to complete 1 lab. How many labs will each of them have run before they meet at the start again?

For x=7 and y=9 Caleb and Eva will meet again. That is, Caleb will have made 7 labs and Eva 9 labs.

Step-by-step explanation:

In order to find the number of labs that Caleb and Eva must complete, to meet again at the start, you can use the following equation:

     (1)

where x is the number of labs made by Caleb and y the number of labs made by Eva. The equation (1) means that for the specific values of x and y, Caleb and Eva will spend the same amount of minutes on the labs.

Then, you need to find the least integers values of x and y.

First, you solve the equation (1) for y:

     (2)

By inspection you can find that the least value of x that makes possible that y is an integer, is 7

In fact, you have:

Hence, for x=7 and y=9 Caleb and Eva will meet again. That is, Caleb will have made 7 labs and Eva 9 labs.