SOLUTION: Apprentice pastry chef Michael takes 9 hours longer than pastry chef Sofia to prepare enough cannoli shells for a wedding. Together, the two can complete the job in 20 hours. How l

Question 682905: Apprentice pastry chef Michael takes 9 hours longer than pastry chef Sofia to prepare enough cannoli shells for a wedding. Together, the two can complete the job in 20 hours. How long does it take each person working alone?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Sofia prepares enough shells in x hours
Then Sophia works at the rate of 1/x of the needed shells per hoour
Michael takes x+9 hours to make enough shells
Then Michael works at the rate of 1/(x+9) of the needed shells per hour
Together they work at the rate of 1/20 of the needed shells per hour,
Soooooo:
1/x + 1/(x+9) =1/20 multiply each term by 20x(x+9)
20(x+9)+20x=x(x+9) get rid of parens
20x+180+20x=x^2+9x simplify
x^2-31x-180=0 quadratic in standard form and it can be factored
(x-36)(x+5)=0
x=36 hours---- time it takes Sophia working alone
x+9=36+9=45 hours ----time it takes Michael working alone
Also
x=-5---------------------no good --can't have negative numbers in this problem
CK
in 20 hours, Sophia does 20/36 of the needed shells
in 20 hours, Michael does 20/45 of the needed shells
20/36+20/45 needs to equal 1 ( all the needed shells, that is)
20/36 +20/45 =1
5/9 +4/9=9/9=1 OKKKKKKKKKK
Hope this helps---ptaylor

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