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gulaghasi [49]
3 years ago
15

Caroline and Chase are working on math homework. They decide to race to see who can finish first. Caroline is on number 12 and c

an 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?​
Mathematics
1 answer:
tiny-mole [99]3 years ago
6 0

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.

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