document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979260>Question 979260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Janene and Emily plan to go on a marathon training run. Emily arrives late, so Janene starts running 16 minute before Emily. Janene runs at an average rate of 9 minutes per mile, and Emily runs at an average rate of 8   1/4   minute per mile. Assuming that both girls started at the same location and ran the same route, how many minutes will Emily take to catch up to Janene? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #600817 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=600817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Janene starts running 16 minute before Emily.<BR>\n" );
document.write( " Janene runs at an average rate of 9 minutes per mile, and Emily runs at an average rate of 8 1/4 minute per mile.<BR>\n" );
document.write( " Assuming that both girls started at the same location and ran the same route, how many minutes will Emily take to catch up to Janene?<BR>\n" );
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document.write( "Let t = time for E to catch J<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+16) = running time for J when she is caught<BR>\n" );
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document.write( "The reciprocal allows us the change their speed to mi per min<BR>\n" );
document.write( "1/9 mi/min is J's speed<BR>\n" );
document.write( "1/8.25 mi/min is E's speed<BR>\n" );
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document.write( "When E catches J, they will have ran the same distance<BR>\n" );
document.write( "Write a distance equation, dist = speed * time<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8.25 ALIGN=MIDDLE  ALT=\"1%2F8.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >(t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >(t+16)<BR>\n" );
document.write( "multiply both sides by the product of 8.25 & 9, results:<BR>\n" );
document.write( "9t = 8.25(t+16)<BR>\n" );
document.write( "9t = 8.25t + 132<BR>\n" );
document.write( "9t - 8.25t = 132<BR>\n" );
document.write( ".75t = 132<BR>\n" );
document.write( "t = 132/.75<BR>\n" );
document.write( "t = 176 minutes for E to Catch J<BR>\n" );
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document.write( "Confirm this by finding the actual distances they ran, should be the same<BR>\n" );
document.write( "J ran 16 + 176 = 192 min<BR>\n" );
document.write( "192 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F9 ALIGN=MIDDLE  ALT=\"1%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 21<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi<BR>\n" );
document.write( "176 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8.25 ALIGN=MIDDLE  ALT=\"1%2F8.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 21<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > mi </SPAN>\n" );
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