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16 Sep 2014, 01:52
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C
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Difficulty:
25%
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Question Stats:
86% (01:57) correct
14%
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wrong
based on 50
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Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?
A. 12 minutes
B. 15 minutes
C. 18 minutes
D. 36 minutes
E. 54 minutes
A. 12 minutes
B. 15 minutes
C. 18 minutes
D. 36 minutes
E. 54 minutes
16 Sep 2014, 01:52
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Official Solution:
Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?
A. 12 minutes
B. 15 minutes
C. 18 minutes
D. 36 minutes
E. 54 minutes
Write each machine's rate as a lowercase letter. We add the rates for each given situation in which machines are working together to load the bin:
\(a + b = \frac{1}{6}\) bin per minute
\(b + c = \frac{1}{9}\) bin per minute
Notice that the rate should always be in "work per time" - in this case, "bins per minute," not "minutes per bin." If it takes machines A and B 6 minutes to load the bin, then they work at a rate of \(\frac{1}{6}\) of a bin per minute.
We are looking for an equation involving the difference of machine A's rate and machine C's rate. In other words, we are looking for \(a - c\). The negative sign in front of the \(c\) indicates that machine C is unloading; in other words, it is working "against" machine A.
We can subtract the two given equations to get the following:
\(a - c = \frac{1}{6} - \frac{1}{9} = \frac{3}{18} - \frac{2}{18} = \frac{1}{18}\) bin per minute.
Thus, it will take 18 minutes for machine A to load the bin, if machine C is simultaneously unloading the bin.
Answer: C
Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?
A. 12 minutes
B. 15 minutes
C. 18 minutes
D. 36 minutes
E. 54 minutes
Write each machine's rate as a lowercase letter. We add the rates for each given situation in which machines are working together to load the bin:
\(a + b = \frac{1}{6}\) bin per minute
\(b + c = \frac{1}{9}\) bin per minute
Notice that the rate should always be in "work per time" - in this case, "bins per minute," not "minutes per bin." If it takes machines A and B 6 minutes to load the bin, then they work at a rate of \(\frac{1}{6}\) of a bin per minute.
We are looking for an equation involving the difference of machine A's rate and machine C's rate. In other words, we are looking for \(a - c\). The negative sign in front of the \(c\) indicates that machine C is unloading; in other words, it is working "against" machine A.
We can subtract the two given equations to get the following:
\(a - c = \frac{1}{6} - \frac{1}{9} = \frac{3}{18} - \frac{2}{18} = \frac{1}{18}\) bin per minute.
Thus, it will take 18 minutes for machine A to load the bin, if machine C is simultaneously unloading the bin.
Answer: C
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