document.write( "Question 463263: An empty bucket put under two faucets. If one faucet is turned on alone,the bucket fills in 6 minutes.if the other faucet is turned on alone,the bucket fills in 4 minutes.if both are turned on,how many seconds will it take to fill the bucket? \n" ); document.write( "

Algebra.Com's Answer #317418 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
An empty bucket put under two faucets. If one faucet is turned on alone,the bucket fills in 6 minutes.if the other faucet is turned on alone,the bucket fills in 4 minutes.if both are turned on,how many seconds will it take to fill the bucket?
\n" ); document.write( "

\r\n" );
document.write( "Two ways, with and without algebra:\r\n" );
document.write( "\r\n" );
document.write( "Without algebra:\r\n" );
document.write( "\r\n" );
document.write( "In 12 minutes the first faucet can fill 2 buckets while the second one\r\n" );
document.write( "fills 3 buckets.  That's 5 buckets in 12 minutes or 1 bucket in 12÷5 \r\n" );
document.write( "or 2.4 minutes.\r\n" );
document.write( "\r\n" );
document.write( "With algebra:\r\n" );
document.write( "\r\n" );
document.write( "Let x be the answer\r\n" );
document.write( "Make this chart:\r\n" );
document.write( "\r\n" );
document.write( "               buckets filled     time    rate in buckets/minute\r\n" );
document.write( "1st faucet           1             6\r\n" );
document.write( "2nd faucet           1             4\r\n" );
document.write( "both open            1             x \r\n" );
document.write( "\r\n" );
document.write( "Fill in the rates by dividing buckets by minutes:\r\n" );
document.write( "\r\n" );
document.write( "               buckets filled     time    rate in buckets/minute\r\n" );
document.write( "1st faucet           1             6             1/6\r\n" );
document.write( "2nd faucet           1             4             1/4\r\n" );
document.write( "both faucets         1             x             1/x\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "   Equation:\r\n" );
document.write( "\r\n" );
document.write( "      1st faucet's rate + 2nd faucet's rate = their combined rate:\r\n" );
document.write( "\r\n" );
document.write( "                    1/6 + 1/4 = 1/x\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 12x\r\n" );
document.write( "\r\n" );
document.write( "                      2x + 3x = 12\r\n" );
document.write( "                           5x = 12\r\n" );
document.write( "                            x = 2.4 minutes.\r\n" );
document.write( "\r\n" );
document.write( "It's easier without algebre, but I assume you are taking algebra.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );