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Together, 15 type A machines and 7 type B machines can

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Together, 15 type A machines and 7 type B machines can

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Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours.

Together 8 type B machines and 15 type C machines can complete the same job in 11 hours.

How many hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?

(A) 22 hours
(B) 30 hours
(C) 44 hours
(D) 60 hours
(E) It cannot be determined from the information above.

OA=C

Source: Veritas Prep

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M7MBA wrote:
Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours.

Together 8 type B machines and 15 type C machines can complete the same job in 11 hours.

How many hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?

(A) 22 hours
(B) 30 hours
(C) 44 hours
(D) 60 hours
(E) It cannot be determined from the information above.
Let the job = 44 units.

Since 15A+7B take 4 hours to complete the 44-unit job, the rate for 15A+7B = w/t = 44/4 = 11 units per hour.
Since 8B+15C take 11 hours to complete the 44-unit job, the rate for 8B+15C = w/t = 44/11 = 4 units per hour.

Adding together 15A+7B=11 and 8B+15C=4, we get:
15A + 15B + 15C = 15 units per hour
A+B+C = 1 unit per hour
Since the rate for A+B+C = 1 unit per hour, the time for A+B+C to complete the 44-unit job = w/r = 44/1 = 44 hours.

The correct answer is C.

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M7MBA wrote:
Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours.

Together 8 type B machines and 15 type C machines can complete the same job in 11 hours.

How many hours would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?

(A) 22 hours
(B) 30 hours
(C) 44 hours
(D) 60 hours
(E) It cannot be determined from the information above.

OA=C

Source: Veritas Prep
Let a, b, and c be the times, in hours, it takes for 1 type A, B, and C machine to finish the job by itself, respectively. So we can create the equations (notice that, for example, 1/a will be the work done by 1 type A machine per hour and n/a will be the work done by n type A machines per hour):

4(15/a) + 4(7/b) = 1

and

11(8/b) + 11(15/c) = 1

If we divide the first equation by 4 and the second by 11, we have:

15/a + 7/b = 1/4

And

8/b + 15/c = 1/11

Now, adding the two new equations, we have:

15/a + 15/b + 15/c = 1/4 + 1/11

15(1/a + 1/b + 1/c) = 15/44

1/a + 1/b + 1/c = 1/44

Thus, the combined rate of 1 type A, B and C machine is 1/44. That is, together they finish 1/44 of the job in one hour. Therefore, it will take them 1/(1/44) = 44 hours to finish the job.

Answer: C

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scott@targettestprep.com



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