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11 Mar 2026, 03:40
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Liam, Emma, and Noah each work at a constant rate and can complete the job alone in 5, 15, and 30 days, respectively. All three begin working together. Liam works for 2 days and then stops, Emma stops working 3 days before the job is completed, and Noah continues working until the job is finished. How many days in total did it take to complete the job?
A. 6 days
B. 7 days
C. 8 days
D. 9 days
E. 12 days
A. 6 days
B. 7 days
C. 8 days
D. 9 days
E. 12 days
11 Mar 2026, 03:40
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Official Solution:
Liam, Emma, and Noah each work at a constant rate and can complete the job alone in 5, 15, and 30 days, respectively. All three begin working together. Liam works for 2 days and then stops, Emma stops working 3 days before the job is completed, and Noah continues working until the job is finished. How many days in total did it take to complete the job?
A. 6 days
B. 7 days
C. 8 days
D. 9 days
E. 12 days
Let total work \(= 1\).
Rates:
Liam \(= \frac{1}{5}\) per day.
Emma \(= \frac{1}{15}\) per day.
Noah \(= \frac{1}{30}\) per day.
Let total time \(= T\) days.
Liam works 2 days: work \(= 2 * \frac{1}{5} = \frac{2}{5}\).
Emma stops 3 days before completion, so she works \(T - 3\) days: work \(= (T - 3) * \frac{1}{15}\).
Noah works the whole time: work \(= T * \frac{1}{30}\).
Thus:
\(\frac{2}{5} + \frac{T - 3}{15} + \frac{T}{30} = 1\).
\(T = 8\).
Answer: C
Liam, Emma, and Noah each work at a constant rate and can complete the job alone in 5, 15, and 30 days, respectively. All three begin working together. Liam works for 2 days and then stops, Emma stops working 3 days before the job is completed, and Noah continues working until the job is finished. How many days in total did it take to complete the job?
A. 6 days
B. 7 days
C. 8 days
D. 9 days
E. 12 days
Let total work \(= 1\).
Rates:
Liam \(= \frac{1}{5}\) per day.
Emma \(= \frac{1}{15}\) per day.
Noah \(= \frac{1}{30}\) per day.
Let total time \(= T\) days.
Liam works 2 days: work \(= 2 * \frac{1}{5} = \frac{2}{5}\).
Emma stops 3 days before completion, so she works \(T - 3\) days: work \(= (T - 3) * \frac{1}{15}\).
Noah works the whole time: work \(= T * \frac{1}{30}\).
Thus:
\(\frac{2}{5} + \frac{T - 3}{15} + \frac{T}{30} = 1\).
\(T = 8\).
Answer: C
