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

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Joined: 15 Jul 2012
Posts: 32
Together, 15 type A machines and 7 type B machines can compl  [#permalink]

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Updated on: 07 Mar 2014, 00:11
1
14
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Difficulty:

65% (hard)

Question Stats:

61% (02:21) correct 39% (02:49) wrong based on 180 sessions

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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.

Originally posted by saggii27 on 06 Mar 2014, 21:44.
Last edited by Bunuel on 07 Mar 2014, 00:11, edited 1 time in total.
Renamed the topic and edited the question.
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Posts: 56371
Re: Together, 15 type A machines and 7 type B machines can compl  [#permalink]

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07 Mar 2014, 00:20
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saggii27 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.

Say the rates of machines A, B and C are a, b, and c, respectively.

Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;

Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.

Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the job in 44 hours.

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Re: Together, 15 type A machines and 7 type B machines can compl  [#permalink]

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03 Aug 2015, 19:08
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saggii27 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.

Since the rates are expressed for a particular job, you should use the work rate formula ==> 1/wr(1) = 1/wr(2) = 1/wr(3) =.....= 1/wr(combined)

In this case we have 15A + 7B = 1/4 (or workrate 1). We also have 8B + 15C = 1/11 (or workrate 2).

Workrates are additive so, we can express the above as: 15A+7B+8B+15C = 1/4 + 1/11 ==> 15A + 15B + 15C = 15/44. This means that using 15 of each machine, we could complete 15 of the particular jobs in 44 hours. The question asks how many hours it would take 1 of each machine to complete 1 job. Dividing 15A + 15B + 15C = 15/44 by 15, gives us A + B + C = 1/44 which means they could complete one job in 44 hours.

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Re: Together, 15 type A machines and 7 type B machines can compl  [#permalink]

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30 Mar 2016, 19:11
saggii27 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.

i thought it might be a trap somewhere..but..if we add both rates, we get:
15A+15B+15C = 1/4+1/11 = 15/44
now, divide by 15 -> 15/44 * 1/15 => rate is 1/44 for A+B+C
so 44 hours,
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Re: Together, 15 type A machines and 7 type B machines can compl  [#permalink]

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16 Apr 2019, 18:00
saggii27 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 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.

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Re: Together, 15 type A machines and 7 type B machines can compl   [#permalink] 16 Apr 2019, 18:00
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