document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170604>Question 1170604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes Robert 9 hours longer to construct a fence than it takes Eldin. If they work together,<BR>\n" );
document.write( "they can construct the fence in 20 hours. How long would it take each, working alone,<BR>\n" );
document.write( "to construct the fence? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795448 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=795448\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = time it takes Eldin to do the job on his own<BR>\n" );
document.write( "x+9 = time it takes Robert to do the job on his own<BR>\n" );
document.write( "x+9 is 9 hours longer compared to x<BR>\n" );
document.write( "x is some positive real number.\r<BR>\n" );
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document.write( "If it takes x hours for Eldin to do the job alone, then his rate is 1/x jobs per hour. Robert's rate is 1/(x+9) jobs per hour if he works alone.\r<BR>\n" );
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document.write( "Their combined rate is 1/x + 1/(x+9)\r<BR>\n" );
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document.write( "This is equal to the combined rate 1/20 since they can get the job done in 20 hours if they work together. One worker must not slow the other down.\r<BR>\n" );
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document.write( "The equation we must solve is<BR>\n" );
document.write( "1/x + 1/(x+9) = 1/20\r<BR>\n" );
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document.write( "Clear out the fractions by multiplying everything by the LCD 20x(x+9)<BR>\n" );
document.write( "Doing so yields the following<BR>\n" );
document.write( "1/x + 1/(x+9) = 1/20<BR>\n" );
document.write( "20x(x+9)*1/x + 20x(x+9)*1/(x+9) = 20x(x+9)*1/20<BR>\n" );
document.write( "20(x+9) + 20x = x(x+9)\r<BR>\n" );
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document.write( "From here let's expand everything out and then get everything to one side<BR>\n" );
document.write( "20(x+9) + 20x = x(x+9)<BR>\n" );
document.write( "20x + 180 + 20x = x^2 + 9x<BR>\n" );
document.write( "40x + 180 = x^2 + 9x<BR>\n" );
document.write( "0 = x^2 + 9x - 40x - 180<BR>\n" );
document.write( "x^2 - 31x - 180 = 0\r<BR>\n" );
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document.write( "We have something of the form <BR>\n" );
document.write( "ax^2 + bx + c = 0<BR>\n" );
document.write( "With a = 1, b = -31, c = -180<BR>\n" );
document.write( "Those three values can be plugged into the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-31%29%2Bsqrt%28%28-31%29%5E2-4%281%29%28-180%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-31%29%2Bsqrt%28%28-31%29%5E2-4%281%29%28-180%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-31%29-sqrt%28%28-31%29%5E2-4%281%29%28-180%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-31%29-sqrt%28%28-31%29%5E2-4%281%29%28-180%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831%2B41%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2831%2B41%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2831-41%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2831-41%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2872%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2872%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-10%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-10%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+36 ALIGN=MIDDLE  ALT=\"x+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-5 ALIGN=MIDDLE  ALT=\"x+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since x must be positive, this rules out the second solution. It makes no sense to have x be negative.\r<BR>\n" );
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document.write( "The only practical solution is x = 36\r<BR>\n" );
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document.write( "It takes Eldin exactly x = 36 hours to do the job on his own<BR>\n" );
document.write( "It takes Robert exactly x+9 = 36+9 = 45 hours to do the job on his own\r<BR>\n" );
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document.write( "Checking the answers:<BR>\n" );
document.write( "1/x + 1/(x+9) = 1/20<BR>\n" );
document.write( "1/36 + 1/(36+9) = 1/20<BR>\n" );
document.write( "1/36 + 1/45 = 1/20<BR>\n" );
document.write( "5/180 + 4/180 = 1/20<BR>\n" );
document.write( "9/180 = 1/20<BR>\n" );
document.write( "1/20 = 1/20<BR>\n" );
document.write( "The answers are confirmed\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "Eldin = 36 hours<BR>\n" );
document.write( "Robert = 45 hours<BR>\n" );
document.write( "Values are exact<BR>\n" );
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document.write( " </SPAN>\n" );
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