SOLUTION: Huck Finn takes five hours longer to paint a fence than it does Tom Sawyer. Together, they can paint the fence in 6 hours. How long would it take each boy working on his own to pai

Question 666799: Huck Finn takes five hours longer to paint a fence than it does Tom Sawyer. Together, they can paint the fence in 6 hours. How long would it take each boy working on his own to paint the fence?
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let x = hours for Tom by himself
Then Huck takes (x + 5)hrs
Let T = the time to take both working together
The formula for Tom and Huck working together is
(1) T = 1/((1/x) + (1/(x+5))) or
(2) T = 1/((x+5 +x)/(x*(x+5))) or
(3) T = (x*(x+5))/(2x+5)
Setting T of (3) equal to the given 6 hrs, we get
(4) 6*(2x+5) = x^2 + 5x or
(5) 12x +30 = x^2 + 5x or
(6) x^2 -7x -30 = 0, which factors to
(7) (x-10)*(x+3) = 0 or
(8) x = {10,-3}
Choosing the positive time as the solution gives
(9) x = 10 hr
Then Huck takes 15 hrs.
Is this right? Check using (1).
Is (6 = 1/((1/10) + (1/15)))?
Is (6 = 1/((10+15)/10*15))?
Is (6 = 150/25)?
Is (6 = 6)? Yes
Answer: Tom Sawyer takes 10 hrs to paint the fence by himself and Huck Finn takes 15 hrs to paint the fence by himself.
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