document.write( "Question 824909: Two pipes can fill a tank in 18 minutes & 27 minutes individually.A third pipe can empty the full tank in 6 minutes.All the three pipes are opened when the tank was 2/3 full.In how many minute will the tank become empty?
\n" ); document.write( "A)11
\n" ); document.write( "B)9 \n" ); document.write( "
Algebra.Com's Answer #496877 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
The above answer is wrong because he goofed in combining the fractions.  He \r\n" );
document.write( "used draining rate as positive and filling rate as negative.  The correction of\r\n" );
document.write( "his method down below the following solution.  But here is my way of working\r\n" );
document.write( "it with explanation: \r\n" );
document.write( "
Two pipes can fill a tank in 18 minutes & 27 minutes individually.
\r\n" );
document.write( "So the rate of the first pipe is 1 tank per 18 minutes,\r\n" );
document.write( "or \"%281_tank%29%2F%2818_minutes%29\", or \"1%2F18\"\"tank%2Fminute\"\r\n" );
document.write( "\r\n" );
document.write( "and the rate of the second pipe is 1 tank per 27 minutes,\r\n" );
document.write( "or \"%281_tank%29%2F%2827_minutes%29\", or \"1%2F27\"\"tank%2Fminute\".
A third pipe can empty the full tank in 6 minutes.
and the rate of the third pipe is the loss of 1 tank or -1 tank per 6 minutes,\r\n" );
document.write( "or \"%28-1_tank%29%2F%286_minutes%29\", or \"-1%2F6\"\"tank%2Fminute\".
All the three pipes are opened when the tank was 2/3 full. \r
\n" ); document.write( "\n" ); document.write( "In how many minute will the tank become empty?
Let the answer be x minutes.\r\n" );
document.write( "\r\n" );
document.write( "Then the combined negative rate of all three pipes is \"-2%2F3\" tank per x minutes,\r\n" );
document.write( "or \"-%28%282%2F3%29tank%29%2F%28x_minutes%29\", or \"-%282%2F3%29%2Fx\"\"tank%2Fminute\" or \"-2%2F%283x%29\"\"tank%2Fminutes\".\r\n" );
document.write( "\r\n" );
document.write( "The equation comes from:\r\n" );
document.write( "\r\n" );
document.write( "\"%28matrix%285%2C1%2C%0D%0Afirst%2C%22pipe%27s%22%2Cpositive%2Cfilling%2C+rate%29%29\"\"%22%22%2B%22%22\"\"%28matrix%285%2C1%2C%0D%0Asecond%2C%22pipe%27s%22%2Cpositive%2Cfilling%2C+rate%29%29\"\"%22%22%2B%22%22\"\"%28matrix%285%2C1%2C%0D%0Athird%2C%22pipe%27s%22%2Cnegative%2Cdraining%2C+rate%29%29\" \"%22%22=%22%22\" \"%28matrix%285%2C1%2C%0D%0Atheir%2Ccombined%2Cnegative%2Cdraining%2C+rate%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%281%2F18%29\"\"%22%22%2B%22%22\"\"%281%2F27%29\"\"%22%22%2B%22%22\"\"%28-1%2F6%29\" \"%22%22=%22%22\" \"-2%2F%283x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%281%2F18%29\"\"%22%22%2B%22%22\"\"%281%2F27%29\"\"%22%22-%22%22\"\"%281%2F6%29\" \"%22%22=%22%22\" \"-2%2F%283x%29\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by LCD = 54x\r\n" );
document.write( "\r\n" );
document.write( "3x + 2x - 9x = -36\r\n" );
document.write( "         -4x = -36\r\n" );
document.write( "           x = 9\r\n" );
document.write( "\r\n" );
document.write( "Answer = 9 minutes.  \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );