document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154837>Question 1154837</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A long-distance runner starts on a course running at an average speed of 6mph. Half an hour later, a second runner begins the same course at an average speed of 7mph. How long after the second runner starts will the second runner overtake the first runner?  </SPAN>\n" );
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document.write( "The second runner starts a half hour after the first.  Since the first runner runs at 6mph, he has run 3 miles when the second runner starts.<br><BR>\n" );
document.write( "The second runner runs 1mph faster than the first.  The amount of time he needs to make up the 3 miles, at the rate of 1mph, is 3 hours.<br><BR>\n" );
document.write( "ANSWER: 3 hours<br><BR>\n" );
document.write( "Algebraically....:<br><BR>\n" );
document.write( "x = hours the second runner runs<BR>\n" );
document.write( "x+0.5 = hours the first runner runs<br><BR>\n" );
document.write( "7x = distance second runner runs<BR>\n" );
document.write( "6(x+0.5) = distance first runner runs.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+=+6%28x%2B0.5%29 ALIGN=MIDDLE  ALT=\"7x+=+6%28x%2B0.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x+=+6x%2B3 ALIGN=MIDDLE  ALT=\"7x+=+6x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );