document.write( "Question 825961: An old machine can do a certain unit of work in 12 hours. To increase production, a more modern machine is put into operation. And both machines now take 4 hours to do the work. If the old machine breaks down, how long will it take the new machine to do the work alone? \n" ); document.write( "

Algebra.Com's Answer #497731 by josmiceli(19441) $\"\"$ $\"About$

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Old machine's rate of working is:
\n" ); document.write( "( 1 unit of work ) / ( 12 hrs )
\n" ); document.write( "Rate of working with both machines:
\n" ); document.write( "( 1 unit of work ) / ( 4 hrs )
\n" ); document.write( "-----------------------------------
\n" ); document.write( "Let the rate of the new machine be:
\n" ); document.write( "( 1 unit of work ) / ( t hrs )
\n" ); document.write( "-----------------------------------
\n" ); document.write( "Add their rates of working to get their
\n" ); document.write( "rate of working together:
\n" ); document.write( " $\"+1%2F12+%2B+1%2Ft+=+1%2F4+\"$
\n" ); document.write( "Multiply both sides by $\"+12t+\"$
\n" ); document.write( " $\"+t+%2B+12+=+3t+\"$
\n" ); document.write( " $\"+2t+=+12+\"$
\n" ); document.write( " $\"+t+=+6+\"$
\n" ); document.write( "The new machine takes 6 hrs to do the work alone
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2F12+%2B+1%2Ft+=+1%2F4+\"$
\n" ); document.write( " $\"+1%2F12+%2B+1%2F6+=+1%2F4+\"$
\n" ); document.write( " $\"+1%2F12+%2B+2%2F12+=+3%2F12+\"$
\n" ); document.write( " $\"+3%2F12+=+3%2F12+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );