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# Mark and Kate individually take 12 hours more and 27 hours more, respe

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Math Expert
Joined: 02 Sep 2009
Posts: 54371
Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

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01 Jul 2017, 03:50
00:00

Difficulty:

45% (medium)

Question Stats:

76% (02:43) correct 24% (02:20) wrong based on 73 sessions

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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

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Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

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01 Jul 2017, 04:19
Lets assume the time they take to do the project to be x.
Hence the time taken by Mark will be x+12 and Kate will be x+27

The work done by both of them in an hour can be written by equation
$$\frac{1}{x} = \frac{1}{x+12} + \frac{1}{x+27}$$
$$(x+12)(x+27) = x(2x+39)$$
$$x^2 + 39x + 324 = 2x^2 + 39x$$
$$x^2 = 324$$
$$x=18$$(because number of hours cannot be negative)

The correct answer is Option C(x=18)
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Re: Mark and Kate individually take 12 hours more and 27 hours more, respe  [#permalink]

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01 Jul 2017, 06:57
Working through options, let's choose 18 first since it's the middle number.

We need to verify if this is true:
$$\frac{1}{18} = \frac{1}{18+12} + \frac{1}{18+27}$$
$$\frac{1}{18} = \frac{1}{30} + \frac{1}{45}$$
$$\frac{1}{18} = \frac{5}{90}$$
$$\frac{1}{18} = \frac{1}{18}$$ - so, this is the correct answer. Ans - C.
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Re: Mark and Kate individually take 12 hours more and 27 hours more, respe   [#permalink] 01 Jul 2017, 06:57
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