document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=186778>Question 186778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rita, Brittany, and Maria can complete a jigsaw puzzle in 1 hour and 30 minutes if they work together. Working alone, it takes Rita 1 less hour to complete the jigsaw puzzle than it takes Brittany, and Brittany completes the jigsaw puzzle three times as fast as Maria. How much time would it take each to complete the jigsaw puzzle working alone\r<BR>\n" );
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document.write( "aND\r<BR>\n" );
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document.write( "Which rational function has a graph with the horizontal asymptote Y=-3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140094 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=140094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rita, Brittany, and Maria can complete a jigsaw puzzle in 1 hour and 30 minutes<BR>\n" );
document.write( " if they work together. Working alone, it takes Rita 1 less hour to complete the<BR>\n" );
document.write( " jigsaw puzzle than it takes Brittany, and Brittany completes the jigsaw puzzle<BR>\n" );
document.write( " three times as fast as Maria. How much time would it take each to complete the<BR>\n" );
document.write( " jigsaw puzzle working alone <BR>\n" );
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document.write( "Let r = time required Rita working alone<BR>\n" );
document.write( "Let b = Brittany alone<BR>\n" );
document.write( "Let m = Maria alone<BR>\n" );
document.write( "Let the completed puzzle = 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2Fr ALIGN=MIDDLE  ALT=\"1.5%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2Fb ALIGN=MIDDLE  ALT=\"1.5%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2Fm ALIGN=MIDDLE  ALT=\"1.5%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "\"it takes Rita 1 less hour to complete the jigsaw puzzle than it takes Brittany,\"<BR>\n" );
document.write( "r = (b-1)<BR>\n" );
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document.write( "\"Brittany completes the jigsaw puzzle  three times as fast as Maria.\"<BR>\n" );
document.write( "m = 3b<BR>\n" );
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document.write( "Substitute for m and r:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2F%28b-1%29 ALIGN=MIDDLE  ALT=\"1.5%2F%28b-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2Fb ALIGN=MIDDLE  ALT=\"1.5%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2F%283b%29 ALIGN=MIDDLE  ALT=\"1.5%2F%283b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by 3b(b-1) to get rid of the denominators, results:<BR>\n" );
document.write( "3b(1.5) + 3(b-1)*1.5 + 1.5(b-1) = 3b(b-1)<BR>\n" );
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document.write( "4.5b + 4.5b - 4.5 + 1.5b - 1.5 = 3b^2 - 3b<BR>\n" );
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document.write( "10.5b - 6 = 3b^2 - 3b<BR>\n" );
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document.write( "0 = 3b^2 - 3b - 10.5b + 6<BR>\n" );
document.write( "A quadratic equation:<BR>\n" );
document.write( "3b^2 - 13.5b + 6 = 0<BR>\n" );
document.write( "Simplify divide eq by 3<BR>\n" );
document.write( "b^2 - 4.5b + 2 = 0<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(b-4)(b-.5) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "b = .5<BR>\n" );
document.write( "b = 4 hrs;  this is the only solution that makes sense<BR>\n" );
document.write( "then<BR>\n" );
document.write( "r = 4 - 1<BR>\n" );
document.write( "r = 3 hrs<BR>\n" );
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document.write( "m = 3(4)<BR>\n" );
document.write( "m = 12 hrs<BR>\n" );
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document.write( "check solution in a calc using the original equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2F3 ALIGN=MIDDLE  ALT=\"1.5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2F4 ALIGN=MIDDLE  ALT=\"1.5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%2F12 ALIGN=MIDDLE  ALT=\"1.5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( ".5 + .375 + .125 = 1<BR>\n" );
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