document.write( "Question 1196841: 3. A tank has two drains. One drain takes 16 minutes longer to empty the tank than does a second drain. With both drains open, the tank is emptied in 6 minutes. How long would it take each drain, working alone, to empty the tank? \n" ); document.write( "
Algebra.Com's Answer #829866 by ankor@dixie-net.com(22740)\"\" \"About 
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3. A tank has two drains.
\n" ); document.write( " One drain takes 16 minutes longer to empty the tank than does a second drain.
\n" ); document.write( " With both drains open, the tank is emptied in 6 minutes.
\n" ); document.write( " How long would it take each drain, working alone, to empty the tank?
\n" ); document.write( ":
\n" ); document.write( "let t = time required by the 2nd drain to empty the tank
\n" ); document.write( "the 1st drain takes 16 min longer, therefore
\n" ); document.write( "(t+16) = time require by the 1st drain to empty the tank
\n" ); document.write( "let the emptied tank = 1
\n" ); document.write( ":
\n" ); document.write( "Each will do a fraction of draining and the two fractions = 1
\n" ); document.write( ":
\n" ); document.write( "\"6%2Ft\" + \"6%2F%28%28t%2B16%29%29\" = 1
\n" ); document.write( "multiply equation by t(t+16), cancel the denominators and we have
\n" ); document.write( "6(t+16) + 6t = t(t+16)
\n" ); document.write( "6t + 96 + 6t = t^2 + 16t
\n" ); document.write( "12t + 96 = t^2 + 16t
\n" ); document.write( "combine to form a quadratic equation on the right
\n" ); document.write( "0 = t^2 + 16t - 12t - 96
\n" ); document.write( "t^2 + 4t - 96 = 0
\n" ); document.write( "this factors to
\n" ); document.write( "(t+12)(t-8) = 0
\n" ); document.write( "the positive solution is what we want here
\n" ); document.write( "t = 8 min is the time of the 2nd drain
\n" ); document.write( "and
\n" ); document.write( "8+16 = 24 min is the time of the 1st drain
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check
\n" ); document.write( "\"6%2F8+%2B+6%2F24\" =
\n" ); document.write( "reduce fractions
\n" ); document.write( "\"3%2F4+%2B+1%2F4\" = 1\r
\n" ); document.write( "\n" ); document.write( ":
\n" ); document.write( " \n" ); document.write( "
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