SOLUTION: A day laborer takes three more days to paint a house than an apprentice painter. A master painter takes three days fewer than the apprentice. The master painter can do as much wor

Question 439251: A day laborer takes three more days to paint a house than an apprentice painter. A master painter takes three days fewer than the apprentice. The master painter can do as much work in seven days as the day laborer and the apprentice working together can accomplish in six days. How long would it take the apprentice alone to paint the house?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes the apprentice to paint the house
Then the apprentice paints at the rate of 1/x house per day
x+3=amount of time needed by the day laborer to paint the house
Then the day laborer works at the rate of 1/(x+3) house per day
x-3=amount of time needed by the master painter to paint the house
Then the master painter works at the rate of 1/(x-3) house per day
In 7 days the master painter can paint 7/(x-3) of the house
In 6 days the apprentice can paint 6/x house
In 6 days the day laborer can paint 6/(x+3) house
Together the day laborer and the apprentice can paint (6/x + 6/(x+3)) house
Now we are told that 7/(x-3)=6/x + 6/(x+3) multiply each term by x(x-3)(x+3)
7x(x+3)=6(x-3)(x+3)+6x(x-3) expand
7x^2+21x=6x^2-54 + 6x^2-18x subtract 7x^2 and also 21x from both sides
0=6x^2-7x^2-21x-54+6x^2-18x or
5x^2-39x-54=0 ---quadratic in standard form
When we solve this quadratic we get:
x=(39+-51)/10
x=-1.2----no good--- can't have negative times
and
x=9----so it takes the apprentice 9 hours to paint the house working alone
It takes the day laborer x+3=9+3=12 hours
And it takes the master painter x-3=9-3=6 hours
CK
In 7 hours the master painter can paint 7/6 house
In 6 hours the apprentice can paint 6/9 house
And in 6 hours the day laborer can paint 6/12 house
Does 6/9 + 6/12 = 7/6 ??
24/36 + 18/36 = 42/36
42/36=42/36
7/6=7/6

Hope this helps----ptaylor

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