Problema Solution
Sam and Shirley own a bakery. Shirley can make a wedding cake in 2 hours less than it takes Sam to make a wedding cake. If they work together, Sam and Shirley can make 5 wedding cakes in 12 hours. How long does it take Sam to make one wedding cake by himself?
Answer provided by our tutors
Let
x = the hours Sam needs to make the cake by himself
1/x cakes per hours = Sam's rate
x - 2 = the hours Shirley needs to make the cake by herself, x - 2 > 0, x > 2
1/(x - 2) cakes per hour = Shirley's rate
(1/x + 1/(x - 2)) cakes per hour = the together rate of Sam and Shirley
Since rate = number of cakes/time we have:
12*(1/x + 1/(x - 2))=5
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click here to see the equation solved for x
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x = 6 hr
We need to ignore the solution 0.8 since we need x>2.
Sam needs 6 hours to make one wedding cake by himself.