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Alecsey
1 month ago
8

Bill, bob, and barry are hired to paint signs. in 8 hours bill can paint 1 sign, bob can paint 2 signs, and barry can paint 1 an

d 1 / 3 signs. they all come to work the first day, but barry doesn't like the job and quits after 3 hours. bob works half an hour longer than barry and quits. how long will it take bill to finish 2 signs they were supposed to paint?
Mathematics
1 answer:
AnnZ [12.3K]1 month ago
7 0

Calculate the rates at which each individual paints.
Bill: x = 1/8 signs/hour
Bob: y = (2 signs)/(8 hours) = 1/4 signs/hour
Barry: z = (4/3 signs)/(8 hours) = 1/6 signs/hour

They need to paint a total of 2 signs cooperatively.

During the first 3 hours, the amount completed is
(x+y+z signs/hour)*(3 hours) = (1/8 + 1/4 + 1/6)*3 = 13/8 signs
Left: 2 - 13/8 = 3/8 signs

Barry leaves the job.
In the following half hour (30 minutes), the total painted is
(x + y signs/hour)*(0.5 hours) = (1/8 + 1/4)*0.5 = 3/16 signs
Left: 3/8 - 3/16 = 3/16 signs

Bob then quits.
The time it takes for Bill to finish the job is
(3/16 signs)/(1/8 signs/hour) = 3/2 hours

Answer: Bill completes the job in 1.5 hours (or 1 hour and 30 minutes).

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