Bunuel wrote:

Mark and Kate individually take 12 hours more and 27 hours more, respectively, to complete a certain project than what they would have taken to complete the same project working together. How many hours do Mark and Kate take to complete the project, working together?

(A) 12

(B) 16

(C) 18

(D) 24

(E) 39

We can let x = the number of hours it would take Mark and Kate to finish the project if they were working together. Thus, Mark’s rate by himself is (x + 12) hours, and Kate’s rate by herself is (x + 27) hours.

Let’s create the equation for their rates. Mark’s rate is 1/(x + 12), Kate’s rate is 1/(x + 27), and their combined rate is 1/x. Thus, we have:

1/(x+12) + 1/(x+27) = 1/x

Multiplying by x(x+27)(x+12) we have:

x(x+27) + x(x+12) = (x+27)(x+12)

x^2 + 27x + x^2 + 12x = x^2 + 39x + 324

x^2 = 324

x = 18

Answer: C

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