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16 Sep 2014, 01:29
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Three workers, A, B, and C, can complete a certain task in 10, 5, and \(x\) hours, respectively. A starts working alone, and after 2 hours, B joins. Two hours later, C joins them. At this point, A, B, and C work together and complete the task in 15 minutes. What is the value of \(x\)?
A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
16 Sep 2014, 01:29
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Official Solution:
Three workers, A, B, and C, can complete a certain task in 10, 5, and \(x\) hours, respectively. A starts working alone, and after 2 hours, B joins. Two hours later, C joins them. At this point, A, B, and C work together and complete the task in 15 minutes. What is the value of \(x\)?
A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
After 2 hours, as only A works during this time, \(2*\frac{1}{10} = \frac{1}{5}\) of the task is completed.
After 4 hours, A and B together complete \(\frac{1}{5} + 2 * (\frac{1}{10} + \frac{1}{5}) = \frac{4}{5}\) of the task, leaving \(\frac{1}{5}\) of the task to be done.
We are told that the remaining \(\frac{1}{5}\) of the task is completed in 15 minutes (or 1/4th of an hour) by all three workers: \(\frac{1}{4} * (\frac{1}{10} + \frac{1}{5} + \frac{1}{x}) = \frac{1}{5}\). From this equation, we can find that \(x = 2\) hours.
Answer: C
Three workers, A, B, and C, can complete a certain task in 10, 5, and \(x\) hours, respectively. A starts working alone, and after 2 hours, B joins. Two hours later, C joins them. At this point, A, B, and C work together and complete the task in 15 minutes. What is the value of \(x\)?
A. \(1\)
B. \(1.25\)
C. \(2\)
D. \(2.5\)
E. \(4\)
After 2 hours, as only A works during this time, \(2*\frac{1}{10} = \frac{1}{5}\) of the task is completed.
After 4 hours, A and B together complete \(\frac{1}{5} + 2 * (\frac{1}{10} + \frac{1}{5}) = \frac{4}{5}\) of the task, leaving \(\frac{1}{5}\) of the task to be done.
We are told that the remaining \(\frac{1}{5}\) of the task is completed in 15 minutes (or 1/4th of an hour) by all three workers: \(\frac{1}{4} * (\frac{1}{10} + \frac{1}{5} + \frac{1}{x}) = \frac{1}{5}\). From this equation, we can find that \(x = 2\) hours.
Answer: C
General Discussion
