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We know that all the machines work at the same rate and we're given two machines working together completes a job in 40 hours. Because the two machines have the same rate, it will take one machine to accomplish the same task twice as long - hence, one machine completes the task in 80 hours. The question asks how many hours it takes 5 similar machines so you divide 80 hours by 5 machines to find the answer. Answer choice D.
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Bunuel
If two identical machines can complete a job in 40 hours, how long, in hours, will it take five such machines to complete the same job?

(A) 4
(B) 8
(C) 10
(D) 16
(E) 20
\(M_1T_1\) \(=\) \(M_2T_2\)

Now, \(2*40\) = \(5T_2\)

So, \(T_2\) \(=\) \(\frac{80}{5}\)

Thus, Answer must be (D)
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Bunuel
If two identical machines can complete a job in 40 hours, how long, in hours, will it take five such machines to complete the same job?

(A) 4
(B) 8
(C) 10
(D) 16
(E) 20
Find and use the rate of one machine to find the time that five machines require to finish.

Rate of ONE machine? W = 1 job
(# of machines) * R * T = W
\(2 * R * 40 = 1\)
\(R=\frac{1}{2*40}=\frac{1}{80}\)


TIME needed for 5 machines at that rate?
(#) * R * T = W
\(5 * \frac{1}{80} * T = 1\)
\(\frac{5}{80} * T = 1\)
\(T = \frac{1}{\frac{5}{80}}=(1* \frac{80}{5})=16\)
hours

Answer D
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Bunuel
If two identical machines can complete a job in 40 hours, how long, in hours, will it take five such machines to complete the same job?

(A) 4
(B) 8
(C) 10
(D) 16
(E) 20

The rate for two machines is 1/40. We can let n = the time it will take 5 machines to complete the job and create the proportion:

2/(1/40) = 5/(1/n)

80 = 5n

16 = n

Answer: D
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Bunuel
If two identical machines can complete a job in 40 hours, how long, in hours, will it take five such machines to complete the same job?

(A) 4
(B) 8
(C) 10
(D) 16
(E) 20

Rate of two machines = 1/40

Rate of one machine = 1/40 * 1/2 = 1/80

Rate of 5 machines = 1/80*5 = 5/80

Work = Rate * Time

1 = 5/80 * Time

Time = 16

(D)
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