document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=324807>Question 324807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After 5 hours of house painting, Jess asked the assistance of Jon. Together, they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours. How long would it have taken Jess to paint the house alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #232570 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=232570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> After 5 hours of house painting, Jess asked the assistance of Jon.<BR>\n" );
document.write( " Together, they finished the job in 4 more hours. <BR>\n" );
document.write( "Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours.<BR>\n" );
document.write( " How long would it have taken Jess to paint the house?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = Jess time painting the house alone<BR>\n" );
document.write( "Let y = Jon's time painting the house<BR>\n" );
document.write( "Let the completed job = 1 (a painted house)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each scenario<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"After 5 hours of house painting, Jess asked the assistance of Jon. Together, they finished the job in 4 more hours.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fx ALIGN=MIDDLE  ALT=\"9%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fy ALIGN=MIDDLE  ALT=\"4%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fx ALIGN=MIDDLE  ALT=\"8%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Fy ALIGN=MIDDLE  ALT=\"7%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can combine the two equations<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fx ALIGN=MIDDLE  ALT=\"9%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fy ALIGN=MIDDLE  ALT=\"4%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fx ALIGN=MIDDLE  ALT=\"8%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Fy ALIGN=MIDDLE  ALT=\"7%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fx ALIGN=MIDDLE  ALT=\"9%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fx ALIGN=MIDDLE  ALT=\"8%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Fy ALIGN=MIDDLE  ALT=\"7%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Fy ALIGN=MIDDLE  ALT=\"4%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fy ALIGN=MIDDLE  ALT=\"3%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cross multiply<BR>\n" );
document.write( "y = 3x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use substitution in the 1st equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Fx ALIGN=MIDDLE  ALT=\"9%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%283x%29 ALIGN=MIDDLE  ALT=\"4%2F%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 <BR>\n" );
document.write( "multiply by 3x, results<BR>\n" );
document.write( "3(9) + 4 = 3x<BR>\n" );
document.write( "27 + 4 = 3x<BR>\n" );
document.write( "31 = 3x<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31%2F3 ALIGN=MIDDLE  ALT=\"31%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 10.3333 hrs (Jess time alone 10<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs)<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "check solution, find y<BR>\n" );
document.write( "y = 3(10.333)<BR>\n" );
document.write( "y = 31 hrs<BR>\n" );
document.write( ":<BR>\n" );
document.write( "check in the 2nd equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F10.333 ALIGN=MIDDLE  ALT=\"8%2F10.333\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F31 ALIGN=MIDDLE  ALT=\"7%2F31\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( ".714 + .226 = 1, confirms our solution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );