SOLUTION: It takes Mr. Soriano 4 days longer to prepare an order of pies than it takes Mrs. Pascual. Together they baked some pies for 2 days and then Mrs. Pascual left. Mr. Soriano took 7 a

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: It takes Mr. Soriano 4 days longer to prepare an order of pies than it takes Mrs. Pascual. Together they baked some pies for 2 days and then Mrs. Pascual left. Mr. Soriano took 7 a      Log On


   

Question 535592: It takes Mr. Soriano 4 days longer to prepare an order of pies than it takes Mrs. Pascual. Together they baked some pies for 2 days and then Mrs. Pascual left. Mr. Soriano took 7 additional days to complete the order of pies. Working alone, how long would it have taken Mrs. Pascual to prepare the pies?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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It takes Mr. Soriano 4 days longer to prepare an order of pies than it takes Mrs. Pascual.
Together they baked some pies for 2 days and then Mrs. Pascual left.
Mr. Soriano took 7 additional days to complete the order of pies.
Working alone, how long would it have taken Mrs. Pascual to prepare the pies?
:
Let p = Mrs. time to make the pies alone
then
(p+4) = Mr. time to do it
Let the completed job = 1, (an order of pies)
:
A shared work equation, Mr. worked to total of 9 days
:
9%2F%28%28p%2B4%29%29 + 2%2Fp = 1
multiply by p(p+4)
9p + 2(p+4) = p(p+4)
9p + 2p + 8 = p^2 + 4p
11p + 8 = p^2 + 4p
combine like terms on the right
0 = p^2 + 4p - 11p - 8
A quadratic equation
p^2 - 7p - 8 = 0
Factors to
(p-8)(p+1) = 0
the positive solution is all we want here
p = 8 days for Mrs. working alone