document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #414696 by DrBeeee(684) $\"\"$ $\"About$

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Let x = hours for Tom by himself
\n" ); document.write( "Then Huck takes (x + 5)hrs
\n" ); document.write( "Let T = the time to take both working together
\n" ); document.write( "The formula for Tom and Huck working together is
\n" ); document.write( "(1) T = 1/((1/x) + (1/(x+5))) or
\n" ); document.write( "(2) T = 1/((x+5 +x)/(x*(x+5))) or
\n" ); document.write( "(3) T = (x*(x+5))/(2x+5)
\n" ); document.write( "Setting T of (3) equal to the given 6 hrs, we get
\n" ); document.write( "(4) 6*(2x+5) = x^2 + 5x or
\n" ); document.write( "(5) 12x +30 = x^2 + 5x or
\n" ); document.write( "(6) x^2 -7x -30 = 0, which factors to
\n" ); document.write( "(7) (x-10)*(x+3) = 0 or
\n" ); document.write( "(8) x = {10,-3}
\n" ); document.write( "Choosing the positive time as the solution gives
\n" ); document.write( "(9) x = 10 hr
\n" ); document.write( "Then Huck takes 15 hrs.
\n" ); document.write( "Is this right? Check using (1).
\n" ); document.write( "Is (6 = 1/((1/10) + (1/15)))?
\n" ); document.write( "Is (6 = 1/((10+15)/10*15))?
\n" ); document.write( "Is (6 = 150/25)?
\n" ); document.write( "Is (6 = 6)? Yes
\n" ); document.write( "Answer: Tom Sawyer takes 10 hrs to paint the fence by himself and Huck Finn takes 15 hrs to paint the fence by himself. \n" ); document.write( "

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