document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149574>Question 149574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A and B working together can do a job in 24 hours.  After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours.  How long would it take each working alone to do the job? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109769 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=109769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A and B working together can do a job in 24 hours.  After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours.  How long would it take each working alone to do the job?<BR>\n" );
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document.write( "Let a = time required when A works alone<BR>\n" );
document.write( "Let b = time required when B works alone<BR>\n" );
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document.write( "Let the completed job = 1<BR>\n" );
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document.write( "write an equation for each scenario :<BR>\n" );
document.write( "\"A and B working together can do a job in 24 hours.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Fa ALIGN=MIDDLE  ALT=\"24%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Fb ALIGN=MIDDLE  ALT=\"24%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by ab to get rid of the denominators, results<BR>\n" );
document.write( "24b + 24a = ab<BR>\n" );
document.write( "24a = ab - 24b<BR>\n" );
document.write( "24a = b(a-24)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24a%2F%28%28a-24%29%29 ALIGN=MIDDLE  ALT=\"24a%2F%28%28a-24%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b  <BR>\n" );
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document.write( "\"After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours.<BR>\n" );
document.write( "That means a worked 27 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2Fa ALIGN=MIDDLE  ALT=\"27%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2Fb ALIGN=MIDDLE  ALT=\"20%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by ab to get rid of the denominators, results<BR>\n" );
document.write( "27b + 20a = ab<BR>\n" );
document.write( "20a = ab - 27b<BR>\n" );
document.write( "20a = b(a-27)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20a%2F%28%28a-27%29%29 ALIGN=MIDDLE  ALT=\"20a%2F%28%28a-27%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b  <BR>\n" );
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document.write( "Therefore:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24a%2F%28%28a-24%29%29 ALIGN=MIDDLE  ALT=\"24a%2F%28%28a-24%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20a%2F%28%28a-27%29%29 ALIGN=MIDDLE  ALT=\"20a%2F%28%28a-27%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply:<BR>\n" );
document.write( "24a(a-27) = 20a(a-24)<BR>\n" );
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document.write( "24a^2 - 648a = 20a^2 - 480a<BR>\n" );
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document.write( "24a^2 - 20a^2 -648a + 480a = 0<BR>\n" );
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document.write( "4a^2 - 168a = 0<BR>\n" );
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document.write( "4a(a - 42) = 0<BR>\n" );
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document.write( "a = +42 A's hrs alone <BR>\n" );
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document.write( "Use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Fa ALIGN=MIDDLE  ALT=\"24%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Fb ALIGN=MIDDLE  ALT=\"24%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 to find b, substitute 42 for a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F42 ALIGN=MIDDLE  ALT=\"24%2F42\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Fb ALIGN=MIDDLE  ALT=\"24%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by 42b<BR>\n" );
document.write( "24b + 42(24) = 42b<BR>\n" );
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document.write( "1008 = 42b - 24b<BR>\n" );
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document.write( "1008 = 18b<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1008%2F18 ALIGN=MIDDLE  ALT=\"1008%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 56 hrs is B's time alone<BR>\n" );
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document.write( "You can check solution using a calc on both equations, a=42, b=56\r<BR>\n" );
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document.write( "   </SPAN>\n" );
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