A, B, and C alone can do a piece of work in 9, 12, and 18 days, respectively. They all started the work together, but A left after 3 days. In how many days, was the total work completed?
24/5
The work done by A, B, and C in one day is:
A's rate = 1/9, B's rate = 1/12, C's rate = 1/18.
The total work done by all three in one day is:
1/9 + 1/12 + 1/18 = 4/36 + 3/36 + 2/36 = 9/36 = 1/4 (Total work per day).
After 3 days, the work done is: 3 * 1/4 = 3/4.
The remaining work = 1 - 3/4 = 1/4.
After A leaves, B and C work together. Their combined rate is:
B + C's rate = 1/12 + 1/18 = 5/36.
The time taken by B and C to complete the remaining work = (1/4) ÷ (5/36) = 36/20 = 9/5 days.
Therefore, the total time taken to complete the work is 3 days (when all worked) + 9/5 days (after A left), which is 24/5 days.
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