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.

Correct answer is C.

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Dennis

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