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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
45% (03:24) correct
55%
(03:31)
wrong
based on 66
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Operating at their respective constant rates, Photocopying machine B takes 6 minutes more than photocopying machine A to copy x pages. When machines A and B are operated simultaneously, 7x pages can be copied in 20 minutes. In how many minutes can machine A operating alone copy 2x pages?
A. 60/7
B. 8
C. 30/7
D. 4
E. A unique answer cannot be determined
A. 60/7
B. 8
C. 30/7
D. 4
E. A unique answer cannot be determined
02 Jan 2023, 21:41
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Bunuel
The stem says:
To copy x pages, machine A takes M minutes.
To copy x pages, machine B takes M + 6 minutes.
To copy 7x pages, machine A and B together take 20 minutes.
This implies that machine A and B together take \(\frac{20}{7}\) minutes to copy x pages.
Once we've known the rate of machine A and B working together to complete copying X pages, to find M, we can use the work rate formula: \(\frac{1}{A} + \frac{1}{B} = \frac{1}{A+B}\)
Plug in the values and then solve the equation to find M:
\(\frac{1}{M} + \frac{1}{M+6} = \frac{7}{20}\)
\(\frac{M+6+M}{M(6+M)} = \frac{7}{20}\)
\(20(M+6+M) = 7(6M+M^2)\)
\(40M+120 = 42M+7M^2\)
\(7M^2 + 2M - 120 = 0\)
\(7M^2 -28M + 30M - 120 = 0\)
\(7M(M - 4) + 30(M - 4) = 0\)
\(M = 4 ,-\frac{30}{7}\) - time cannot be negative, so we can get rid of the negative value.
Now we know that machine A takes 4 minutes to complete copying x pages; however, this is not what the question asks.
The question asks "how many minutes does machine A takes to complete copying 2x pages?; so, we need to multiply M by 2.
Therefore, the correct answer is 8 minutes.
PS. I'd like to know whether there are more efficient ways to solve this kind of questions.
samarpan.g28
28 Jan 2024, 08:23
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Bunuel
Time=1/Efficiency.
Let A take t mins, B take t+6 mins. Total efficiency {1/t + 1/(t+6)}. This is the efficiency of copying x pages together.
Given, to copy 7x pages, they take 20 mins. So to copy x pages they take 20/7 mins. Therefore total efficiency is 7/20.
{1/t + 1/(t+6)} = 7/20. Simply solving for t, we get t=4 and -(30/7), ignore the latter one.
So the time to copy x pages for A is t=4 mins. Therefore, for 2x pages, A takes 2*4=8 mins(B).
