document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=754070>Question 754070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alicia can complete a certain project in 5 more hours than her brother Alex if they work together they can finish the job in 6 hours, How long would it take each one of them to complete the project?\\r<BR>\n" );
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document.write( "Can you please help me out ? Thanks so much in advance:)<BR>\n" );
document.write( "Can you also please show the steps it would really help me understand better:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458773 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=458773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Alicia can complete a certain project in 5 more hours than her brother Alex<BR>\n" );
document.write( " if they work together they can finish the job in 6 hours, How long would it take each one of them to complete the project?\ <BR>\n" );
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document.write( "Let x = time required by Alex to do the job<BR>\n" );
document.write( "It says,\"Alicia can complete a certain project in 5 more hours than<BR>\n" );
document.write( " her brother\". Therefore<BR>\n" );
document.write( "(x+5) = time required by Alicia to do the job<BR>\n" );
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document.write( "let the completed job = 1<BR>\n" );
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document.write( "Write a shared work equation, each does a fraction of the job<BR>\n" );
document.write( "the two fractions add up to 1<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Fx ALIGN=MIDDLE  ALT=\"6%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"6%2F%28%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 <BR>\n" );
document.write( "Multiply by x(x+5), cancel the denominators, and you have:<BR>\n" );
document.write( "6(x+5) + 6x = x(x+5)<BR>\n" );
document.write( "6x + 30 + 6x = x^2 + 5x<BR>\n" );
document.write( "Combine as a quadratic equation on the right:<BR>\n" );
document.write( "0 = x^2 + 5x - 12x - 30<BR>\n" );
document.write( "x^2 - 7x - 30 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x-10)(x+3) = 0<BR>\n" );
document.write( "The positive solution is all we want here<BR>\n" );
document.write( "x = 10 hrs required by Alex<BR>\n" );
document.write( "then<BR>\n" );
document.write( "15 hrs required by Alicia<BR>\n" );
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document.write( "See if this checks out<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F10 ALIGN=MIDDLE  ALT=\"6%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F15 ALIGN=MIDDLE  ALT=\"6%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( ".6 + .4 = 1; confirms our solution </SPAN>\n" );
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