Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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?​

Sagot :

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.

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.