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C
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Difficulty:
65%
(hard)
Question Stats:
64% (02:18) correct
36%
(02:41)
wrong
based on 674
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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.
(A) 22 hours
(B) 30 hours
(C) 44 hours
(D) 60 hours
(E) It cannot be determined from the information above.
07 Mar 2014, 00:20
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saggii27
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.
Answer: C.
General Discussion
03 Aug 2015, 19:08
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saggii27
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.
Correct answer is C.
