document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=244764>Question 244764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"It took a faster runner 10 seconds longer to run a distance of 1500 feet than it took a slower runner to run a distance of 1000 feet. if the rate of the faster runner was 5 ft/s more than the rate of the slower runner, what was the rate of each?\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178978 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=178978\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"It took a faster runner 10 seconds longer to run a distance of 1500 feet than it took a slower runner to run a distance of 1000 feet.<BR>\n" );
document.write( "Let t = time in sec for the faster runner to run 1500 ft<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t-10) = time of the slower runner to run 1000 ft<BR>\n" );
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document.write( "if the rate of the faster runner was 5 ft/s more than the rate of the slower runner, what was the rate of each?\"<BR>\n" );
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document.write( "Write a rate equation: Rate = dist/time:<BR>\n" );
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document.write( "Fast rate - slow rate = 5 ft/sec<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500%2Ft ALIGN=MIDDLE  ALT=\"1500%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000%2F%28t-10%29 ALIGN=MIDDLE  ALT=\"1000%2F%28t-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
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document.write( "Multiply equation by t(t-10), results<BR>\n" );
document.write( "1500(t-10) - 1000t = 5t(t-10)<BR>\n" );
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document.write( "1500t - 15000 - 1000t = 5t^2 - 50t<BR>\n" );
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document.write( "500t - 15000 = 5t^2 - 50t<BR>\n" );
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document.write( "0 = 5t^2 - 50t - 500t + 15000<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "5t^2 - 550t + 15000 = 0<BR>\n" );
document.write( "Simplify, divide by 5<BR>\n" );
document.write( "t^2 - 110t + 3000 = 0<BR>\n" );
document.write( "Factor to<BR>\n" );
document.write( "(t - 50)(t - 60) = 0<BR>\n" );
document.write( "two solutions<BR>\n" );
document.write( "t = 50 sec<BR>\n" );
document.write( "t = 60 sec<BR>\n" );
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document.write( "Assume t = 50<BR>\n" );
document.write( "1500/50 = 30 ft/sec for the fast guy<BR>\n" );
document.write( "and<BR>\n" );
document.write( "1000/40 = 25 ft/sec for the slow guy (5 ft/sec slower)<BR>\n" );
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document.write( "You can check the other solution </SPAN>\n" );
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