A can complete a job in 9 days, while each of B and C can complete it in 18 days. All three start working together and work for x days. Then A leaves, and B and C together finish the remaining work in x days. Find the value of x.
3
Write each person's one-day work as a fraction of the job. A does \(\frac{1}{9}\), while B and C each do \(\frac{1}{18}\).
Combined rate of all three = \(\frac{1}{9} + \frac{1}{18} + \frac{1}{18} = \frac{2}{18} + \frac{1}{18} + \frac{1}{18} = \frac{4}{18} = \frac{2}{9}\).
In the first x days they complete \(\frac{2}{9} \times x = \frac{2x}{9}\) of the work.
After A leaves, B and C together work at \(\frac{1}{18} + \frac{1}{18} = \frac{1}{9}\) per day, and in x days they complete \(\frac{x}{9}\).
The whole job is done, so \(\frac{2x}{9} + \frac{x}{9} = 1\), giving \(\frac{3x}{9} = 1\).
Thus \(\frac{x}{3} = 1\), so \(x = 3\).
Hence, the value of x is 3.
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