document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182671>Question 182671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One painter takes 6 hours longer to paint a room than does a second painter.  Working together, they can paint the room in 4 hours.  How long wouold it take each painter working alone to paint the room? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137160 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=137160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One painter takes 6 hours longer to paint a room than does a second painter. Working together, they can paint the room in 4 hours. How long wouold it take each painter working alone to paint the room?<BR>\n" );
document.write( "-----------------------------------------------------<BR>\n" );
document.write( "2nd painter DATA:<BR>\n" );
document.write( "time = x hr/job ; rate = 1/x job/hr<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "1st painter DATA:<BR>\n" );
document.write( "time = (x+6) hr/job ; rate = 1/(x+6) job/hr<BR>\n" );
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document.write( "Together DATA:<BR>\n" );
document.write( "time = 4 hr/job ; rate = 1/4 job/hr<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "rate + rate = together rate<BR>\n" );
document.write( "1/x + 1/(x+6) = 1/4\r<BR>\n" );
document.write( "\n" );
document.write( "Multiply thru by 4x(x+6) to get:<BR>\n" );
document.write( "4(x+6) + 4x = x(x+6)<BR>\n" );
document.write( "4x + 24 + 4x = x^2 + 6x<BR>\n" );
document.write( "x^2 -2x - 24 = 0<BR>\n" );
document.write( "(x-6)(x+4) = 0<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "x = 6 hrs (time for 2nd painter to do the job alone)<BR>\n" );
document.write( "x+6= 12 hrs (time for the 1st to do the job alone)<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );