Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Select the correct answer. Sean and Colleen are raking leaves in their yard. Working together, they can clear the yard of leaves in 24 minutes. Working alone, it would take Sean 20 minutes longer to clear the yard than it would take Colleen working alone. When c is the number of minutes it would take Colleen to finish the job when working alone, the situation is modeled by this rational equation: How long would it take Colleen alone to clear the yard of leaves?

Sagot :

raphealnwobi

Answer:

40 minutes

Step-by-step explanation:

Let c represent the number of minutes it would take colleen to finish the job when he is working alone. Hence, it can be represented by the equation:

[tex]\frac{1}{c}+\frac{1}{c+20} =\frac{1}{24} \\\\Finding\ the\ L.C.M\ of\ the\ fraction\ to\ get\ 24c(c+20)\ as\ the\ L.C.M.\\Multiply\ the\ whole\ equation\ by\ 24c(c+20):\\\\\frac{1}{c}(24c(c+20))+\frac{1}{c+20}(24c(c+20)) =\frac{1}{24}(24c(c+20)) \\\\24c+480+24c=c^2+20c\\\\48c+480=c^2+20c\\\\c^2+20c-48c-480=0\\\\c^2-28c-480=0[/tex]

Solving the quadratic equation to get c gives:

c = -12 and c = 40

Since the time cannot be negative, hence c = 40 minutes.

It would take colleen 40 minutes to clear the yard of leaves alone

View image raphealnwobi
queenava4l

Answer:

40 minutes

Step-by-step explanation:

I got it right on my test.

View image queenava4l
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.