document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239722>Question 239722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My parents have to paint their house.  If my son painted it alone it would take him 4 hours longer than I would take.  However, if he worked with me, he would work twice as fast.  Develop a formula for how long it would take both of us working together.  Simplify/reduce to lowest terms. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175972 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=175972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  If my son painted it alone it would take him 4 hours longer than I would take. However, if he worked with me, he would work twice as fast. Develop a formula for how long it would take both of us working together. Simplify/reduce to lowest terms.<BR>\n" );
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document.write( "Let x = time required by you working alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+4) = time required by son working alone<BR>\n" );
document.write( ".5(x+4) = time if he worked twice as fast<BR>\n" );
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document.write( "Let y = time working together<BR>\n" );
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document.write( "Let the completed job = 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fx ALIGN=MIDDLE  ALT=\"y%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F%28.5%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"y%2F%28.5%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "multiply both sides .5x(x+4)<BR>\n" );
document.write( ".5(x+4)y + xy = .5x(x+4)<BR>\n" );
document.write( "Factor out y<BR>\n" );
document.write( "y(.5(x+4) + x) = .5x(x+4)<BR>\n" );
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document.write( "y(.5x + 2 + x) = .5x^2 + 2x<BR>\n" );
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document.write( "y(1.5x + 2) = .5x^2 + 2x<BR>\n" );
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document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.5x%5E2+%2B+2x%29%2F%281.5x+%2B+2%29 ALIGN=MIDDLE  ALT=\"%28.5x%5E2+%2B+2x%29%2F%281.5x+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where <BR>\n" );
document.write( "y = hrs when working together using Dad's time working alone (x)<BR>\n" );
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document.write( "Prove that, assume dad can do it in 12 hrs, x = 12, find y<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.5%2812%5E2%29+%2B+2%2812%29%29%2F%281.5%2812%29+%2B+2%29 ALIGN=MIDDLE  ALT=\"%28.5%2812%5E2%29+%2B+2%2812%29%29%2F%281.5%2812%29+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.5%28144%29+%2B+24%29%2F%2818+%2B+2%29 ALIGN=MIDDLE  ALT=\"%28.5%28144%29+%2B+24%29%2F%2818+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2872+%2B+24%29%2F%2820%29 ALIGN=MIDDLE  ALT=\"%2872+%2B+24%29%2F%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 96/20<BR>\n" );
document.write( "y = 4.8 hrs working together<BR>\n" );
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document.write( "Check this in the shared work equation (son's time .5(12+4) = 8 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.8%2F12 ALIGN=MIDDLE  ALT=\"4.8%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.8%2F8 ALIGN=MIDDLE  ALT=\"4.8%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".4 + .6 = 1; the completed job!<BR>\n" );
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document.write( "Interesting that the son does more work than the dad except when dad does the job in 4 hrs, then they share the work equally, and do it in two hours<BR>\n" );
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document.write( "An interesting problem, thanks for submitting it. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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