document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374130>Question 374130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Together Gunther and Gerta can peel a bushel of potatoes in 48 minutes. Working alone, it takes Gerta 28 minutes longer than Gunther to peel a bushel of potatoes. How long would it take for Gunther to do this job by himself? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266260 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=266260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Together Gunther and Gerta can peel a bushel of potatoes in 48 minutes.<BR>\n" );
document.write( " Working alone, it takes Gerta 28 minutes longer than Gunther to peel a bushel of potatoes. <BR>\n" );
document.write( "How long would it take for Gunther to do this job by himself?<BR>\n" );
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document.write( "Let g = Gun's time alone<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(g+28) = Gert's time alone<BR>\n" );
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document.write( "Let the completed job = 1<BR>\n" );
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document.write( "A typical shared work equation, each will do a fraction of the job, 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=48%2Fg ALIGN=MIDDLE  ALT=\"48%2Fg\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48%2F%28%28g%2B28%29%29 ALIGN=MIDDLE  ALT=\"48%2F%28%28g%2B28%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by g(g+28) results:<BR>\n" );
document.write( "48(g+28) + 48g = g(g+28)<BR>\n" );
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document.write( "48g + 1344 + 48g = g^2 + 28g<BR>\n" );
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document.write( "96g + 1344 = g^2 + 28g<BR>\n" );
document.write( "Arrange as a quadratic equation on the right:<BR>\n" );
document.write( "0 = g^2 + 28g - 96g - 1344<BR>\n" );
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document.write( "g^2 - 68g - 1344 = 0<BR>\n" );
document.write( "you can use the quadratic formula to find g, but this will factor to:<BR>\n" );
document.write( "(g-84)(g+16) = 0<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "g = 84 minutes, Gun's time alone<BR>\n" );
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document.write( "Check solution<BR>\n" );
document.write( "48/84 + 48/112 = <BR>\n" );
document.write( ".57 + .43 = 1.00, confirms our solution  </SPAN>\n" );
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