# math

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If painter A can paint a room in three hours by themselves, and painter B can paint the same room in four hours, and painter C can paint the same room in six hours, how long will it take for all three to paint the room together if they do not get in each others way? Thanks

• math -

This problem can be solved by working out the fraction of work done by each worker in one hour.

For A, fraction of work done per hour is 1/3.
For B, 1/4.
For C, 1/6.

If they all work together, in one hour they would have done
(1/3+1/4+1/6)
= (4+3+2)/12
= 9/12
= 3/4
of the work.

So if they paint together, it would take them 1/(3/4) = 4/3 days.

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