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If 6 machines of type A can complete a certain job in 15 days, working alone at their respective constant rates, and 9 machines of type B can do the same job in 12 days, then how long would it take 2 machines of type A and 3 machines of type B, working together, to complete the same job?
(A) 36
(B) 30
(C) 24
(D) 20
(E) 18
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(A) 36
(B) 30
(C) 24
(D) 20
(E) 18
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Finding rate of a single machine A:
\(\frac{6}{x}=\frac{1}{15}\)
\(x = 90\) days for one machine to finish the job.
Finding rate of a single machine B:
\(\frac{9}{x}=\frac{1}{12}\)
\(x = 108\) days for one machine to finish the job.
How long would it take 2 machines of type A and 3 machines of type B, working together, to complete the same job?:
\(\frac{2}{90}+ \frac{3}{108} = \frac{1}{c}\)
\(\frac{12+15}{540} = \frac{1}{c}\)
\(\frac{27}{540} = \frac{1}{c}\)
\(27c = 540\)
\(c = 20\)
Answer D
\(\frac{6}{x}=\frac{1}{15}\)
\(x = 90\) days for one machine to finish the job.
Finding rate of a single machine B:
\(\frac{9}{x}=\frac{1}{12}\)
\(x = 108\) days for one machine to finish the job.
How long would it take 2 machines of type A and 3 machines of type B, working together, to complete the same job?:
\(\frac{2}{90}+ \frac{3}{108} = \frac{1}{c}\)
\(\frac{12+15}{540} = \frac{1}{c}\)
\(\frac{27}{540} = \frac{1}{c}\)
\(27c = 540\)
\(c = 20\)
Answer D
Schools: Sloan (MIT)
Posts: 22
Assume N units of work. Make N as lcm of 6,15,9,12 for ease of calculation. LCM(6,15,9,12) = 180.
So, assume total work to be 180 units.
6 machines of A can do it in 15 day => 1 A can do 2 units/day.
9 machines of B can do it in 12 days => 1 B can do 5/3 units/day
Combined rate of 2 As and 3 Bs: 2A + 3B = 2x2 + 3(5/3) = 9 units/day
There are 180 units, so 180/9 = 20 days for 2A & 3B together to do the work!
So, assume total work to be 180 units.
6 machines of A can do it in 15 day => 1 A can do 2 units/day.
9 machines of B can do it in 12 days => 1 B can do 5/3 units/day
Combined rate of 2 As and 3 Bs: 2A + 3B = 2x2 + 3(5/3) = 9 units/day
There are 180 units, so 180/9 = 20 days for 2A & 3B together to do the work!
Work problems is about rate and productivity is work/time
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