A can complete a work in 10 day, B in 12 days and C in 15 days. All of them began the work together , but A had to leave the work after 2 days of start and B in 3 days before the completion of work. How log did the work last?
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First 2 days all three of them worked together, thus they did 2*(1/10 + 1/12 + 1/15) = 1/2 of the work.
Last 3 days only Carla worked, thus she did 3/15 = 1/5 of the work.
1 - 1/2 - 1/5 = 3/10 of the work was done by Ben and Carla: (time)*(combined rate)=(job done) --> t*(1/12 + 1/15) = 3/10 --> t = 2 days. So, we have that Ben and Carla worked together for 2 days.
Total days = 2 + 3 + 2 = 7.
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