document.write( "Question 633181: It takes one painter 20 hours longer to paint a house than it does a more experienced painter. Together they can paint a house in 24 hours. How long does it take each painter to paint the house working alone? \n" ); document.write( "

Algebra.Com's Answer #398702 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = the time it takes the more experienced painter
\n" ); document.write( "to paint the house
\n" ); document.write( " $\"+t+%2B+20+\"$ = time for less experienced painter
\n" ); document.write( "---------
\n" ); document.write( "Add their rates of painting to get rate working together
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t+%2B+20+%29+=+1%2F24+\"$
\n" ); document.write( "Multiply both sides by $\"+120t%2A%28+t+%2B+20+%29+\"$
\n" ); document.write( " $\"+120%2A%28+t+%2B+20+%29+%2B+120t++=+5t%2A%28+t+%2B+20+%29+\"$
\n" ); document.write( " $\"+120t+%2B+2400+%2B+120t+=+5t%5E2+%2B+100t+\"$
\n" ); document.write( " $\"+5t%5E2+-+140t+-+2400+=+0+\"$
\n" ); document.write( " $\"+t%5E2+-+28t+-+480+=+0+\"$
\n" ); document.write( " $\"+t%5E2+-++28t+=+480+\"$
\n" ); document.write( "Complete the square
\n" ); document.write( " $\"+t%5E2+-+28t+%2B+%2828%2F2%29%5E2+=+480+%2B+%2828%2F2%29%5E2+\"$
\n" ); document.write( " $\"+t%5E2+-+28t+%2B+196+=+676+\"$
\n" ); document.write( " $\"+%28+t+-+14+%29%5E2++=+26%5E2+\"$
\n" ); document.write( " $\"+t+-+14+=+26+\"$
\n" ); document.write( " $\"+t+=+40+\"$
\n" ); document.write( "40 hrs = the time it takes the more experienced painter
\n" ); document.write( "to paint the house
\n" ); document.write( "60 hrs = time for less experienced painter \n" ); document.write( "

\n" );