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15 May 2015, 03:36
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D
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Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 3x boxes?
A. 3 minutes
B. 4 minutes
C. 5 minutes
D. 6 minutes
E. 12 minutes
A. 3 minutes
B. 4 minutes
C. 5 minutes
D. 6 minutes
E. 12 minutes
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21 Oct 2023, 09:21
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Official Solution:
Working alone at its constant rate, machine A produces \(x\) boxes in 10 minutes and working alone at its constant rate, machine B produces \(2x\) boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce \(3x\) boxes?
A. 3 minutes
B. 4 minutes
C. 5 minutes
D. 6 minutes
E. 12 minutes
The rate of machine A = \(\frac{job \ done}{time} = \frac{x}{10}\) boxes per minute.
The rate of machine B = \(\frac{job \ done}{time} = \frac{2x}{5}\) boxes per minute.
Their combined rate is \(\frac{x}{10} + \frac{2x}{5} = \frac{x}{2}\) boxes per minute.
To produce \(3x\) boxes, together they will need \(time = \frac{job \ done}{combined \ rate} = \frac{3x}{(\frac{x}{2})} = 6\) minutes.
Answer: D
Working alone at its constant rate, machine A produces \(x\) boxes in 10 minutes and working alone at its constant rate, machine B produces \(2x\) boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce \(3x\) boxes?
A. 3 minutes
B. 4 minutes
C. 5 minutes
D. 6 minutes
E. 12 minutes
The rate of machine A = \(\frac{job \ done}{time} = \frac{x}{10}\) boxes per minute.
The rate of machine B = \(\frac{job \ done}{time} = \frac{2x}{5}\) boxes per minute.
Their combined rate is \(\frac{x}{10} + \frac{2x}{5} = \frac{x}{2}\) boxes per minute.
To produce \(3x\) boxes, together they will need \(time = \frac{job \ done}{combined \ rate} = \frac{3x}{(\frac{x}{2})} = 6\) minutes.
Answer: D
General Discussion
15 May 2015, 03:46
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Bunuel
Plug in 10 for x to make it easier.
Machine 1 produces at a rate of 10/10 = 1 box per minute
Machine 2 produces at a rate of 20/5 = 4 boxes per minute
Combined Rate is 5 boxes per minute
Therefore both machines take 3x = 30 boxes / 5 = 6 minutes
