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 [tex]\frac{1}{1.5} = \frac{2}{3}[/tex] of a problem. So, after t minutes, she will be on the problem:
[tex]Ca(t) = 12 + \frac{2t}{3}[/tex]
Chase is on number 16 and can solve 1 math problem in 2 minutes.
Per minute, he solved [tex]\frac{1}{2}[/tex] of a problem. So, after t minutes, he will be on the problem:
[tex]Ch(t) = 16 + \frac{t}{2}[/tex]
How many minutes will it take before they are on the same problem?
This is t for which:
[tex]Ca(t) = Ch(t)[/tex]
So
[tex]12 + \frac{2t}{3} = 16 + \frac{t}{2}[/tex]
[tex]\frac{2t}{3} - \frac{t}{2} = 4[/tex]
[tex]\frac{4t-3t}{6} = 4[/tex]
[tex]\frac{t}{6} = 4[/tex]
[tex]t = 24[/tex]
It will take 24 minutes before they are on the same problem.
