Question

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?

Answer 1

40 minutes

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:

`(1)/(c)+(1)/(c+20) =(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):\\\\(1)/(c)(24c(c+20))+(1)/(c+20)(24c(c+20)) =(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`

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