document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854340>Question 854340</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 16 hours. If Ralph paints alone for 25 minutes before Lisa begins helping, how long must they work together to finish painting the fence? Give your answer as a simplified fraction.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514619 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ralph's rate of painting is:<BR>\n" );
document.write( "( 1 fence ) / ( 14 hrs )<BR>\n" );
document.write( "He paints the fence alone for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25%2F60+=+5%2F12+ ALIGN=MIDDLE  ALT=\"+25%2F60+=+5%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr<BR>\n" );
document.write( "I can say:<BR>\n" );
document.write( "( fraction of the fence he paints ) = ( his rate of painting ) x ( time spent painting )<BR>\n" );
document.write( "fraction of the fence he paints = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+1%2F14+%29%2A%28+5%2F12+%29+=+5%2F168+ ALIGN=MIDDLE  ALT=\"+%28+1%2F14+%29%2A%28+5%2F12+%29+=+5%2F168+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That means there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+-+5%2F168+=+163%2F168+ ALIGN=MIDDLE  ALT=\"+1+-+5%2F168+=+163%2F168+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "of the fence left to paint<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the time in hours for them to paint <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+163%2F168+ ALIGN=MIDDLE  ALT=\"+163%2F168+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "of the fence painting together<BR>\n" );
document.write( "Add their rates of painting to find rate painting together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F14+%2B+1%2F16+=+%28+163%2F168+%29+%2F+t+ ALIGN=MIDDLE  ALT=\"+1%2F14+%2B+1%2F16+=+%28+163%2F168+%29+%2F+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+168%2A2%2At+=+336t+ ALIGN=MIDDLE  ALT=\"+168%2A2%2At+=+336t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+24t+%2B+21t+=+326+ ALIGN=MIDDLE  ALT=\"+24t+%2B+21t+=+326+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+45t+=+326+ ALIGN=MIDDLE  ALT=\"+45t+=+326+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+7.2444+ ALIGN=MIDDLE  ALT=\"+t+=+7.2444+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.2444%2A60+=+14.667+ ALIGN=MIDDLE  ALT=\"+.2444%2A60+=+14.667+\"   DISABLED_style= \"max-width:90%; height:auto;\" > min<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "Working together, they finish the fence in 7 hrs 14 min 40 sec<BR>\n" );
document.write( "As a simplified fraction, expressed in hours, this is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+326%2F45+ ALIGN=MIDDLE  ALT=\"+326%2F45+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "check answer using calculator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F14+%2B+1%2F16+=+%28+163%2F168+%29+%2F+t+ ALIGN=MIDDLE  ALT=\"+1%2F14+%2B+1%2F16+=+%28+163%2F168+%29+%2F+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F14+%2B+1%2F16+=+%28+163%2F168+%29+%2F+%28+326%2F45+%29+ ALIGN=MIDDLE  ALT=\"+1%2F14+%2B+1%2F16+=+%28+163%2F168+%29+%2F+%28+326%2F45+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.071429+%2B+.0625+=+.97024+%2F+7.2444+ ALIGN=MIDDLE  ALT=\"+.071429+%2B+.0625+=+.97024+%2F+7.2444+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.133929+=+.133929+ ALIGN=MIDDLE  ALT=\"+.133929+=+.133929+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );