document.write( "Question 143802: It takes 2 hours and 24 minutes for Gail and Bob to paint a room together.
\n" ); document.write( "If painting alone, it would take Bob 2 hours more to paint the room than
\n" ); document.write( "it would take Gail. How long does it take Gail to paint the room?
\n" ); document.write( "Please provide the equation necessary to solve.\r
\n" ); document.write( "\n" ); document.write( "I know the answer is 4 hours, but I need to show my work. Thanks!! \n" ); document.write( "
Algebra.Com's Answer #104646 by ankor@dixie-net.com(22740)\"\" \"About 
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It takes 2 hours and 24 minutes for Gail and Bob to paint a room together.
\n" ); document.write( "If painting alone, it would take Bob 2 hours more to paint the room than
\n" ); document.write( "it would take Gail. How long does it take Gail to paint the room?
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\n" ); document.write( "Convert 2 hr 24 min to hrs; 2 + 24/60 = 2.4 hrs
\n" ); document.write( ":
\n" ); document.write( "Let x = time required for G to paint the room alone
\n" ); document.write( ":
\n" ); document.write( "It says it takes B two hrs longer to do the job, therefore:
\n" ); document.write( "(x+2) = B's time to paint it alone
\n" ); document.write( ":
\n" ); document.write( "Let the completed job = 1
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\n" ); document.write( "Write an equation representing the fraction painted by each person:
\n" ); document.write( ";
\n" ); document.write( "\"2.4%2F%28%28x%2B2%29%29\" + \"2.4%2Fx\" = 1
\n" ); document.write( "Multiply equation by x(x+2) to eliminate the denominators:
\n" ); document.write( "x(x+2)*\"2.4%2F%28%28x%2B2%29%29\" + x(x+2)*\"2.4%2Fx\" = x(x+2)(1)
\n" ); document.write( "cancel the denominators and you have:
\n" ); document.write( ":
\n" ); document.write( "2.4x + 2.4(x+2) = x(x+2)
\n" ); document.write( ":
\n" ); document.write( "2.4x + 2.4x + 4.8 = x^2 + 2x
\n" ); document.write( ":
\n" ); document.write( "4.8x + 4.8 = x^2 + 2x
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\n" ); document.write( "Arrange as a quadratic equation:
\n" ); document.write( "x^2 + 2x - 4.8x - 4.8 = 0
\n" ); document.write( ":
\n" ); document.write( "x^2 - 2.8x - 4.8 = 0
\n" ); document.write( ":
\n" ); document.write( "Use the quadratic formula to find the solution:
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "In this equation: a=1; b=-2.8; c=-4.8
\n" ); document.write( "\"x+=+%28-%28-2.8%29+%2B-+sqrt%28-2.8%5E2+-+4+%2A+1+%2A-4.8+%29%29%2F%282%2A1%29+\"
\n" ); document.write( "\"x+=+%282.8+%2B-+sqrt%287.84+%2B+19.2%29%29%2F%282%29+\"
\n" ); document.write( "You can do the math, the positive solution should be x = 4
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