document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818401>Question 818401</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pat and Jane want to paint a fence, pat can paint the fence by himself in 3 hours, jane can paint the fence by herself in 4 hours. At noon, they start painting the fence together. At some point, they argue for ten minutes, and no painting gets done. After the arguement, jane leaves and pat paints alone. If pat finishes painting at 2:25 pm, at what time did the argument begin? How do u solve.....is it a work rate problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492550 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=492550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it's a work problem that is divided<BR>\n" );
document.write( "into 3 parts:<BR>\n" );
document.write( "(1) painting done by both<BR>\n" );
document.write( "(2) short period of no painting<BR>\n" );
document.write( "(3) painting done by Pat alone<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the amount of time in hours<BR>\n" );
document.write( "from noon to when they started their<BR>\n" );
document.write( "10 minute argument<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the amount of time in hours<BR>\n" );
document.write( "from the end of the 10 minute argument<BR>\n" );
document.write( "to 2:25 PM<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the fraction of the job that they<BR>\n" );
document.write( "both get done in the 1st time period<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+-+x+ ALIGN=MIDDLE  ALT=\"+1+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the fraction of the job that<BR>\n" );
document.write( "Pat does in the 3rd time period<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "For the 1st time period, I can say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F3+%2B+1%2F4+=+x%2Ft%5B1%5D+ ALIGN=MIDDLE  ALT=\"+1%2F3+%2B+1%2F4+=+x%2Ft%5B1%5D+\"   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=+12+ ALIGN=MIDDLE  ALT=\"+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+%2B+3+=+12%2A%28+x%2Ft%5B1%5D%29+ ALIGN=MIDDLE  ALT=\"+4+%2B+3+=+12%2A%28+x%2Ft%5B1%5D%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2Ft%5B1%5D+=+7%2F12+ ALIGN=MIDDLE  ALT=\"+x%2Ft%5B1%5D+=+7%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+=+%2812%2F7%29%2Ax+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+=+%2812%2F7%29%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Fot the 3rd time period:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+=+%28+1-x+%29+%2F+t%5B2%5D+ ALIGN=MIDDLE  ALT=\"+1%2F4+=+%28+1-x+%29+%2F+t%5B2%5D+\"   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=+4%2At%5B2%5D+ ALIGN=MIDDLE  ALT=\"+4%2At%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+=+4%2A%28+1-x+%29+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+4%2A%28+1-x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+=+4+-+4x+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+4+-+4x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "So far I have 2 equations and 3 unknowns.<BR>\n" );
document.write( "The 3rd equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+1%2F6+%2B+t%5B2%5D+=+2+%2B+5%2F12+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+1%2F6+%2B+t%5B2%5D+=+2+%2B+5%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( note that I converted minutes to hours )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+t%5B2%5D+=+2+%2B+5%2F12+-+2%2F12++ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+t%5B2%5D+=+2+%2B+5%2F12+-+2%2F12++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+t%5B2%5D+=+27%2F12+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+t%5B2%5D+=+27%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute (a) and (b) into (c)<BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2812%2F7%29%2Ax+%2B+4+-+4x+=+9%2F4+ ALIGN=MIDDLE  ALT=\"+%2812%2F7%29%2Ax+%2B+4+-+4x+=+9%2F4+\"   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=+28+ ALIGN=MIDDLE  ALT=\"+28+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+48x+%2B+112+-+112x+=+63+ ALIGN=MIDDLE  ALT=\"+48x+%2B+112+-+112x+=+63+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+64x+=+112+-+63+ ALIGN=MIDDLE  ALT=\"+64x+=+112+-+63+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+64x+=+49+ ALIGN=MIDDLE  ALT=\"+64x+=+49+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+49%2F64+ ALIGN=MIDDLE  ALT=\"+x+=+49%2F64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+=+%2812%2F7%29%2Ax+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+=+%2812%2F7%29%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+=+%2812%2F7%29%2A%2849%2F64%29+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+=+%2812%2F7%29%2A%2849%2F64%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+=+84%2F64+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+=+84%2F64+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+=+21%2F16+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+=+21%2F16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+=+4+-+4x+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+4+-+4x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+=+4+-+4%2A%2849%2F64%29+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+4+-+4%2A%2849%2F64%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+=+4%2A%28+1+-+49%2F64+%29+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+4%2A%28+1+-+49%2F64+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+=+4%2A%28+15%2F64+%29+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+4%2A%28+15%2F64+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B2%5D+=+15%2F16+ ALIGN=MIDDLE  ALT=\"+t%5B2%5D+=+15%2F16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+%2B+1%2F6+%2B+t%5B2%5D+=+2+%2B+5%2F12+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+%2B+1%2F6+%2B+t%5B2%5D+=+2+%2B+5%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21%2F16+%2B+1%2F6+%2B+15%2F16+=+2+%2B+5%2F12+ ALIGN=MIDDLE  ALT=\"+21%2F16+%2B+1%2F6+%2B+15%2F16+=+2+%2B+5%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36%2F16+=+2+%2B+5%2F12+-+2%2F12+ ALIGN=MIDDLE  ALT=\"+36%2F16+=+2+%2B+5%2F12+-+2%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+36%2F16+=+27%2F12+ ALIGN=MIDDLE  ALT=\"+36%2F16+=+27%2F12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%2F4+=+9%2F4+ ALIGN=MIDDLE  ALT=\"+9%2F4+=+9%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "Noon plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5B1%5D+ ALIGN=MIDDLE  ALT=\"+t%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21%2F16+ ALIGN=MIDDLE  ALT=\"+21%2F16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21%2F16+=+16%2F16+%2B+5%2F16+ ALIGN=MIDDLE  ALT=\"+21%2F16+=+16%2F16+%2B+5%2F16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%2F16%29%2A60+=+18.75+ ALIGN=MIDDLE  ALT=\"+%285%2F16%29%2A60+=+18.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.75%2A60+=+45+ ALIGN=MIDDLE  ALT=\"+.75%2A60+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The argument began at 1:18:45<BR>\n" );
document.write( "Unless I made a mistake- check the work<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );