A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in ____?
Answer: 6 days
Explanation
A and B together can complete the work in 3 days, so their combined rate of work is 1/3 per day.
They work together for 2 days, so they complete 2/3 of the work.
B leaves, and A completes the remaining 1/3 of the work in 2 days. This means A's rate of work is 1/6 per day (since A completes 1/3 of the work in 2 days).
Now, we know B's rate of work is the difference between their combined rate and A's rate: (1/3 - 1/6) = 1/6 per day.
Since B can complete the entire work in x days, B's rate of work is also 1/x per day.
Equating the two expressions for B's rate of work, we get: 1/6 = 1/x --> x = 6
So, B alone can complete the work in 6 days.
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