Question

Caroline and Chase are working on math homework. They decide to race to see who can finish first. Caroline is on number 12 and can solve 1 math problem in 1.5 minutes. Chase is on number 16 and can solve 1 math problem in 2 minutes. How many minutes will it take before they are on the same problem?​

Answer 1

It will take 24 minutes before they are on the same problem.

Explanation:

Caroline is on number 12 and can solve 1 math problem in 1.5 minutes.

Per minute, she solved
`(1)/(1.5) = (2)/(3)` of a problem. So, after t minutes, she will be on the problem:

`Ca(t) = 12 + (2t)/(3)`

Chase is on number 16 and can solve 1 math problem in 2 minutes.

Per minute, he solved
`(1)/(2)` of a problem. So, after t minutes, he will be on the problem:

`Ch(t) = 16 + (t)/(2)`

How many minutes will it take before they are on the same problem?​

This is t for which:

`Ca(t) = Ch(t)`

So

`12 + (2t)/(3) = 16 + (t)/(2)`

`(2t)/(3) - (t)/(2) = 4`

`(4t-3t)/(6) = 4`

`(t)/(6) = 4`

`t = 24`

It will take 24 minutes before they are on the same problem.