document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572524>Question 572524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tom, dick, and harry paint houses. If all three work together, they finish in five days. If tom and dick work together they finish in eight days. If tom and harry work together they finish in ten days. How long would it take each one alone to paint a house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368562 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=368562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tom, dick, and harry paint houses.<BR>\n" );
document.write( " If all three work together, they finish in five days.<BR>\n" );
document.write( " If tom and dick work together they finish in eight days.<BR>\n" );
document.write( " If tom and harry work together they finish in ten days. <BR>\n" );
document.write( "How long would it take each one alone to paint a house?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let t = Tom's time to paint the house alone<BR>\n" );
document.write( "Let d = Dick's time<BR>\n" );
document.write( "Let h = Harry's time<BR>\n" );
document.write( "Let the competed job = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a shared work equation for each scenario<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Tom, dick, and harry paint houses. If all three work together, they finish in five days.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ft ALIGN=MIDDLE  ALT=\"5%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fd ALIGN=MIDDLE  ALT=\"5%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fh ALIGN=MIDDLE  ALT=\"5%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ";<BR>\n" );
document.write( "\" If tom and dick work together they finish in eight days.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ft ALIGN=MIDDLE  ALT=\"8%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Fd ALIGN=MIDDLE  ALT=\"8%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"If tom and harry work together they finish in ten days.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ft ALIGN=MIDDLE  ALT=\"10%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fh ALIGN=MIDDLE  ALT=\"10%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can use elimination here, mult the 1st eq by 2, subtract the 3rd eq<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ft ALIGN=MIDDLE  ALT=\"10%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fd ALIGN=MIDDLE  ALT=\"10%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fh ALIGN=MIDDLE  ALT=\"10%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Ft ALIGN=MIDDLE  ALT=\"10%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Fd ALIGN=MIDDLE  ALT=\"0%2Fd\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fh ALIGN=MIDDLE  ALT=\"10%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "-------------------------------------------subtraction eliminates t and h<BR>\n" );
document.write( "10/d = 1<BR>\n" );
document.write( "multiply both sides by d<BR>\n" );
document.write( "d = 10 days for Dick to do the job alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the 2nd equation to find t<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2Ft ALIGN=MIDDLE  ALT=\"8%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F10 ALIGN=MIDDLE  ALT=\"8%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1;  <BR>\n" );
document.write( "multiply by 10t, results:<BR>\n" );
document.write( "10(8) + t(8) = 10t<BR>\n" );
document.write( "80 = 10t - 8t<BR>\n" );
document.write( "80 = 2t<BR>\n" );
document.write( "t = 40 days for Tom to do the job alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the 3rd equation to find h<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F40 ALIGN=MIDDLE  ALT=\"10%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fh ALIGN=MIDDLE  ALT=\"10%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 <BR>\n" );
document.write( "multiply by 40h<BR>\n" );
document.write( "10h + 40(10) = 40h<BR>\n" );
document.write( "400 = 40h - 10h<BR>\n" );
document.write( "400 = 30h<BR>\n" );
document.write( "h = 400/30<BR>\n" );
document.write( "h = 13<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;\" > days for Harry to do the job alone<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let's see if this checks out using decimals in the 1st equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F40 ALIGN=MIDDLE  ALT=\"5%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F10 ALIGN=MIDDLE  ALT=\"5%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F13.33 ALIGN=MIDDLE  ALT=\"5%2F13.33\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ".125 + .50 + .375 = 1; confirms our solutions of:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Tom takes 40 days, rather useless<BR>\n" );
document.write( "Dick takes 10 days, carrying the load<BR>\n" );
document.write( "Harry takes 13 1/3 days, a good helper\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );