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.
Answer: C
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