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Andreas and Bruno each work at a constant rate. Andreas can clear a garden plot working alone in 50 days. He works for 5 days and then leaves. The remaining work is cleared by Bruno working alone in 30 days. In how many days can Andreas and Bruno clear the entire plot if they work together from the start?
A. \(16 \frac{2}{3}\)
B. \(18 \frac{3}{4}\)
C. \(20\)
D. \(22 \frac{1}{2}\)
E. \(25\)
A. \(16 \frac{2}{3}\)
B. \(18 \frac{3}{4}\)
C. \(20\)
D. \(22 \frac{1}{2}\)
E. \(25\)
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Official Solution:
Andreas and Bruno each work at a constant rate. Andreas can clear a garden plot working alone in 50 days. He works for 5 days and then leaves. The remaining work is cleared by Bruno working alone in 30 days. In how many days can Andreas and Bruno clear the entire plot if they work together from the start?
A. \(16 \frac{2}{3}\)
B. \(18 \frac{3}{4}\)
C. \(20\)
D. \(22 \frac{1}{2}\)
E. \(25\)
Total work \(= 1\).
Andreas rate \(= \frac{1}{50}\).
Work done in 5 days \(= 5 * \frac{1}{50} = \frac{1}{10}\).
Remaining work \(= 1 - \frac{1}{10} = \frac{9}{10}\).
Bruno does \(\frac{9}{10}\) in 30 days.
Bruno rate \(= \frac{\frac{9}{10}}{30} = \frac{9}{300} = \frac{3}{100}\).
Together rate \(= \frac{1}{50} + \frac{3}{100} = \frac{1}{20}\).
Time together \(= \frac{1}{\frac{1}{20}} = 20\).
Answer: C
Andreas and Bruno each work at a constant rate. Andreas can clear a garden plot working alone in 50 days. He works for 5 days and then leaves. The remaining work is cleared by Bruno working alone in 30 days. In how many days can Andreas and Bruno clear the entire plot if they work together from the start?
A. \(16 \frac{2}{3}\)
B. \(18 \frac{3}{4}\)
C. \(20\)
D. \(22 \frac{1}{2}\)
E. \(25\)
Total work \(= 1\).
Andreas rate \(= \frac{1}{50}\).
Work done in 5 days \(= 5 * \frac{1}{50} = \frac{1}{10}\).
Remaining work \(= 1 - \frac{1}{10} = \frac{9}{10}\).
Bruno does \(\frac{9}{10}\) in 30 days.
Bruno rate \(= \frac{\frac{9}{10}}{30} = \frac{9}{300} = \frac{3}{100}\).
Together rate \(= \frac{1}{50} + \frac{3}{100} = \frac{1}{20}\).
Time together \(= \frac{1}{\frac{1}{20}} = 20\).
Answer: C
