Thread: Word Problem, Machines working at rates

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Word Problem, Machines working at rates

Can anybody tell me how to solve this problem?

Machines A and B always operate independently and at their respective constant rates. When working alone, machine A can fill a production lot in 5 hours, and machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x?

A) 3 1/3
B) 3
C) 2 1/2
D) 2 1/3
E) 1 1/2

Answer is A, how do I get that though?

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Machine A in one hour: 1/5 of the work.
Machine B in one hour: 1/x of the work.

When they work together: 1/5 + 1/x = (x+5)/5x. You take the reciprocal to obtain the time. In general:

• If A can do a work in x days and B can do the same work in y days, then A and B can together do the work in (xy)/(x+y) days

Productivity of A: 1/5
Productivity of B: 1/x

AB/(A+B) = 2 ==> 5B/(5+B) = 2 ==> B = 10/3 = 3 1/3. Answer A.

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Thanks!!

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