document.write( "Question 273955: please help me solve this word problem: two pipes working together drain a water holding tank in 6 hours. if used alone to empty the tank, one takes 2 hours longer than the other. how long does each take to empty the tank if used alone? \n" ); document.write( "
Algebra.Com's Answer #200024 by ankor@dixie-net.com(22740)\"\" \"About 
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two pipes working together drain a water holding tank in 6 hours.
\n" ); document.write( " if used alone to empty the tank, one takes 2 hours longer than the other.
\n" ); document.write( " how long does each take to empty the tank if used alone?
\n" ); document.write( ":
\n" ); document.write( "Let x = time for one pipe to drain it by itself
\n" ); document.write( "then
\n" ); document.write( "(x+2) = time for the other pipe to by itself
\n" ); document.write( ";
\n" ); document.write( "Let the completed job = 1, (a drained tank)
\n" ); document.write( ":
\n" ); document.write( "Each pipe does a fraction of the job, the two fractions add up to one.
\n" ); document.write( "\"6%2Fx\" + \"6%2F%28%28x%2B2%29%29\" = 1
\n" ); document.write( "Multiply equation by x(x+2), results:
\n" ); document.write( "6(x+2) + 6x = x(x+2)
\n" ); document.write( ";
\n" ); document.write( "6x + 12 + 6x = x^2 + 2x
\n" ); document.write( ":
\n" ); document.write( "12x + 12 = x^2 + 2x
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "0 = x^2 + 2x - 12x - 12
\n" ); document.write( ":
\n" ); document.write( "x^2 - 10x - 12 = 0
\n" ); document.write( "We have to use the quadratic formula to solve this:
\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=-10; c=-12
\n" ); document.write( "\"x+=+%28-%28-10%29+%2B-+sqrt%28-10%5E2-4%2A1%2A-12+%29%29%2F%282%2A1%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%2810+%2B-+sqrt%28100+-%28-48%29+%29%29%2F2+\"
\n" ); document.write( "\"x+=+%2810+%2B-+sqrt%28100+%2B+48+%29%29%2F2+\"
\n" ); document.write( "\"x+=+%2810+%2B-+sqrt%28148+%29%29%2F2+\"
\n" ); document.write( "We only want the positive solution
\n" ); document.write( "\"x+=+%2810+%2B+12.1655%29%2F2+\"
\n" ); document.write( "x = \"22.1655%2F2\"
\n" ); document.write( "x = 11.08 hrs, for the 1st pipe to drain it alone
\n" ); document.write( "and
\n" ); document.write( "11.08 + 2 = 13.08 hrs for the 2nd pipe alone
\n" ); document.write( ";
\n" ); document.write( ":
\n" ); document.write( "Check solution
\n" ); document.write( "6/11.08 + 6/13.08 =
\n" ); document.write( ".54 + .46 = 1; confirms our solutions \n" ); document.write( "
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