document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969588>Question 969588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The time required for the examinees to solve the same problem differs by two minutes. Together they can solve 32 problems in one hour. How long will it take for the slower problem solver to solve a problem? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592471 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=592471\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The time required for the examinees to solve the same problem differs by two minutes.<BR>\n" );
document.write( " Together they can solve 32 problems in one hour.<BR>\n" );
document.write( " How long will it take for the slower problem solver to solve a problem?<BR>\n" );
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document.write( "Find how many minutes per problem when they work together, 1 hr = 60 min<BR>\n" );
document.write( "60/32 = 1.875 minutes per problem\r<BR>\n" );
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document.write( "Let t = time required by the slower solver in minutes<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t-2) = time required by the faster solver<BR>\n" );
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document.write( "let the completed job = 1, (one problem solved)<BR>\n" );
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document.write( "A shared work equation to solve 1 problem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.875%2Ft ALIGN=MIDDLE  ALT=\"1.875%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.875%2F%28%28t-2%29%29 ALIGN=MIDDLE  ALT=\"1.875%2F%28%28t-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply equation by t(t-2), cancel the denominators, and you have:<BR>\n" );
document.write( "1.875(t-2) + 1.875t = t(t-2)<BR>\n" );
document.write( "1.875t - 3.75 + 1.875t = t^2 - 2t <BR>\n" );
document.write( "3.75t - 3.75 = t^2 - 2t<BR>\n" );
document.write( "combine to form a quadratic equation on the right<BR>\n" );
document.write( "0 = t^2 - 2t - 3.75t + 3.75 <BR>\n" );
document.write( "t^2 - 5.75t + 3.75 = 0<BR>\n" );
document.write( "using the quadratic formula, a=1; b=-5.75; c=3.75<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "t = .75, not reasonable<BR>\n" );
document.write( "t = 5 minutes a reasonable solution, slower guy per problem<BR>\n" );
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document.write( "See if that works out, find how many each can solve in 60 min<BR>\n" );
document.write( "We know the faster guy takes 2 min less or 3 min per problem<BR>\n" );
document.write( "60/3 = 20 problems<BR>\n" );
document.write( "60/5 = 12 problems<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "total: 32 problems<BR>\n" );
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document.write( "Did all this make sense to you? ankor@att.net </SPAN>\n" );
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