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

Answer:

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

Step-by-step explanation:

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

Per minute, she solved $\frac{1}{1.5} = \frac{2}{3}$ of a problem. So, after t minutes, she will be on the problem:

$Ca(t) = 12 + \frac{2t}{3}$

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

Per minute, he solved $\frac{1}{2}$ of a problem. So, after t minutes, he will be on the problem:

$Ch(t) = 16 + \frac{t}{2}$

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

This is t for which:

$Ca(t) = Ch(t)$

So

$12 + \frac{2t}{3} = 16 + \frac{t}{2}$

$\frac{2t}{3} - \frac{t}{2} = 4$

$\frac{4t-3t}{6} = 4$

$\frac{t}{6} = 4$

$t = 24$

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