document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=329121>Question 329121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My father-in-law used to have a garden in our backyard. We worried about him weeding the whole garden by himself so we usually sent one of our children out to help. Now, if my son worked on the garden by himself it would take him 4 hours longer to weed the garden than his grandfather took. However, if he worked with my father-in-law, he worked twice as fast. Develop a formula for how long it took for both of them to weed the whole garden working together. Simplify/reduce to lowest terms.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235917 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=235917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if my son worked on the garden by himself it would take him 4 hours longer to weed the garden than his grandfather took. However, if he worked with my father-in-law, he worked twice as fast. Develop a formula for how long it took for both of them to weed the whole garden working together. Simplify/reduce to lowest terms.<BR>\n" );
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document.write( "Let x = time required by son working alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x-4) = time required by grandad alone<BR>\n" );
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document.write( "If son works twice as fast: <BR>\n" );
document.write( ".5x = time when son working with grandad<BR>\n" );
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document.write( "Let completed job = 1 (A weeded garden)<BR>\n" );
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document.write( "Let t = time to complete the job working together<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F%28%28x-4%29%29 ALIGN=MIDDLE  ALT=\"t%2F%28%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F%28.5x%29 ALIGN=MIDDLE  ALT=\"t%2F%28.5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Multiply by .5x(x-4), results<BR>\n" );
document.write( ".5xt + t(x-4) = .5x(x-4)<BR>\n" );
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document.write( ".5xt + xt - 4t = .5x^2 - 2x<BR>\n" );
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document.write( "1.5xt - 4t = .5x^2 - 2x<BR>\n" );
document.write( "Factor out t<BR>\n" );
document.write( "t(1.5x - 4) = .5x^2 - 2x<BR>\n" );
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document.write( "Divide both sides by (1.5x-4)<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28.5x%5E2-2x%29%29%2F%28%281.5x-4%29%29 ALIGN=MIDDLE  ALT=\"%28%28.5x%5E2-2x%29%29%2F%28%281.5x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is the formula<BR>\n" );
document.write( "where:<BR>\n" );
document.write( "t = time working together<BR>\n" );
document.write( "x = son's time working alone<BR>\n" );
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