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Question 1034412: solve. Round to the nearest tenth of necessary
Mr. Endicott, Mr. Bookout, and Mr. Piatt are going to paint a house together. Mr. Endicott can paint one side of the house in 4 hrs. to paint an equal area, Mr. Bookout takes 3 hrs and Mr. Piatt takes 2 hrs. If the men work together, how long will it take them to paint one side of the house?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! e = the rate that mr. endicott can paint the side of a house.
b = the rate that mr. bookout can paint the side of a house.
p = the rate that mr. piatt can paint the side of a house.
e = 1/4
b = 1/3
p = 1/2
this is derived from the general formula of r * t = q
r is the rate of work.
t is the time.
q is the quantity of work.
q = 1 side of a house.
t = number of hours to paint the side of the house.
r is the rate at which the side of the house is painted.
for mr. endicott, the formula becomes r * 4 = 1
solve for r to get 1/4.
do the same for mr. bookman and mr. piatt and you get the rates shown above.
when they work together, their rates are additive.
you get (r1 + r2 + r2) * t = q
q = 1
r1 = e = 1/4
r2 = b = 1/3
r3 = p = 1/2
you get (1/4 + 1/3 + 1/2) * t = 1
least common denominator looks to be 12.
you get (3/12 + 4/12 + 6/12) * t = 1
combine like terms to get 13/12 * t = 1
divide both sides of the equation by 13/12 to get t = 1 / (13/12)
this is the same as t = 1 * (12/13) = 12/13
it would take them 12/13 of an hour to paint the side of the house if they all work together.
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