SOLUTION: Bill, Bob, and Barry are painting signs. In 8 hours Bill can paint 1 sign,Bob can paint 2, and Barry can paint 1 and 1/3 signs. Barry stops painting after 3 hours, and Bob stops af

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Question 996903: Bill, Bob, and Barry are painting signs. In 8 hours Bill can paint 1 sign,Bob can paint 2, and Barry can paint 1 and 1/3 signs. Barry stops painting after 3 hours, and Bob stops after 3 and 1/2. How long will it it take Bill to finish the 2 signs they had to do
Answer by josgarithmetic(39844) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify their rates. 

           raw        step            simplified
Bill      1%2F8           1%2F8            1%2F8
Bob       2%2F8           1%2F4            1%2F4
Barry     %281%2B1%2F3%29%2F8     %284%2F3%29%2F8          1%2F6


Review the time sequence and who is working. The description is obscure but we might guess that the job begins with all three people working.
Bill+Bob+Barry work for 3 hours;
Barry stops, and
Bill+Bob work for 3+1/2 hours;
Bob stops, and
Bill works for some unknown t time in hours to do "2 signs they had to do".


Again, this seems an obscure description, but seems like the amount of work to do was to be 2 signs. The unit in the rate table is in SIGN per HOUR. This should likely be the amount of job or work to be done from the beginning.


Put the time sequence into an equation.
.
This is what you basically want to setup; and then solve it for t.

(I leave the arithmetic steps for you to do).