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16 Sep 2014, 00:12
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Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together 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, 00:12
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Official Solution:
Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together 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, A, working alone, completes \(2*\frac{1}{10}=\frac{1}{5}\) of the task;
After 4 hours, a total of \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task is completed, with A and B working together for the last 2 hours, leaving \(\frac{1}{5}\) of the task remaining;
We know that the final \(\frac{1}{5}\) of the task is completed in 15 minutes (or \(\frac{1}{4}\) 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 determine that \(x=2\) hours.
Answer: C
Three workers, A, B, and C, can finish a task in 10, 5, and \(x\) hours respectively. A begins working alone, and after 2 hours, B joins in. Another two hours later, C joins them, and all three together 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, A, working alone, completes \(2*\frac{1}{10}=\frac{1}{5}\) of the task;
After 4 hours, a total of \(\frac{1}{5}+2*(\frac{1}{10}+\frac{1}{5})=\frac{4}{5}\) of the task is completed, with A and B working together for the last 2 hours, leaving \(\frac{1}{5}\) of the task remaining;
We know that the final \(\frac{1}{5}\) of the task is completed in 15 minutes (or \(\frac{1}{4}\) 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 determine that \(x=2\) hours.
Answer: C
General Discussion
31 Oct 2015, 21:04
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A works alone for 2 hours,
0.2x(work) completed
joins B
0.2x completed by worker A
1/5 => 2/5 completed or 0.4x completed by worker B
after 4 hours we have 0.8x completed
joins C and everything is finished in 15 minutes
or 0.2x (work) is completed in 0.25 hours
now we can set an equation
1/10 + 1/5+ 1/x = 2/10 * 4/1 simplify 1/5 or 4/5
multiply everyting by 10
1+2+10/x = 8
10/x = 5
x = 2.
0.2x(work) completed
joins B
0.2x completed by worker A
1/5 => 2/5 completed or 0.4x completed by worker B
after 4 hours we have 0.8x completed
joins C and everything is finished in 15 minutes
or 0.2x (work) is completed in 0.25 hours
now we can set an equation
1/10 + 1/5+ 1/x = 2/10 * 4/1 simplify 1/5 or 4/5
multiply everyting by 10
1+2+10/x = 8
10/x = 5
x = 2.
