document.write( "Question 692040: It takes one painter 20 hours longer to pain a hoise than it does a more experienced painter. Together they paint the house in 24 hours. How long does it take for each painter to paint the house working alone? \n" ); document.write( "

Algebra.Com's Answer #426931 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = time in hours for experienced painter
\n" ); document.write( "to paint house
\n" ); document.write( " $\"+t+%2B+20+\"$ = other painter's time in hours to paint house
\n" ); document.write( "Add their rates of painting to get rate working together
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t+%2B+20+%29+=+1%2F+24+\"$
\n" ); document.write( "Multiply both sides by $\"+24t%2A%28+t+%2B+20+%29+\"$
\n" ); document.write( " $\"+24%2A%28+t%2B20+%29+%2B+24t+=+t%2A%28+t%2B20+%29+\"$
\n" ); document.write( " $\"+24t+%2B+480+%2B+24t+=+t%5E2+%2B+20t+\"$
\n" ); document.write( " $\"+t%5E2+-+28t+-+480+=+0+\"$
\n" ); document.write( "I'll complete the square
\n" ); document.write( " $\"+t%5E2+-+28t+=+480++\"$
\n" ); document.write( " $\"+t%5E2+-+28t+%2B+%2828%2F2%29%5E2+=+480+%2B+%2828%2F2%29%5E2+\"$
\n" ); document.write( " $\"+t%5E2+-+28t+%2B+196+=+480+%2B+196+\"$
\n" ); document.write( " $\"+%28+t+-+14+%29%5E2+=+676+\"$
\n" ); document.write( " $\"+t+-+14+=+26+\"$
\n" ); document.write( " $\"+t+=+40+\"$
\n" ); document.write( " $\"+t+%2B+20+=+60+\"$
\n" ); document.write( "It takes them 40 hrs for experienced painter
\n" ); document.write( "and 60 hrs for other painter
\n" ); document.write( "check:
\n" ); document.write( " $\"+1%2Ft+%2B+1%2F%28+t+%2B+20+%29+=+1%2F+24+\"$
\n" ); document.write( " $\"+1%2F40%2B+1%2F60+=+1%2F+24+\"$
\n" ); document.write( "Multiply both sides by $\"120\"$
\n" ); document.write( " $\"+3+%2B+2+=+5+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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