document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218393>Question 218393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the question reads: In a bicycle race, Lionel gives Robert a 500 meter advantage. Lionel also agrees to start 15 minutes after Robert. If Lionel bikes at 17 km/h and Robert at 14 km/h how long will it take Lionel after he starts biking to overtake Robert?\r<BR>\n" );
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document.write( "so I set up a chart:\r<BR>\n" );
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document.write( "           Time     x     Rate     = Distance<BR>\n" );
document.write( "Lionel     t+1/4           17          d + 1/2 (km)<BR>\n" );
document.write( "Robert       t             14          d\r<BR>\n" );
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document.write( "then I have the equations:\r<BR>\n" );
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document.write( "17(t+1/4) = d + 1/2      and      14t=d\r<BR>\n" );
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document.write( "so I solve:\r<BR>\n" );
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document.write( "17t + 17/4 = 14t + 1/2<BR>\n" );
document.write( "3t = -15/4<BR>\n" );
document.write( "and i get t = to a negative number\r<BR>\n" );
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document.write( "how is that possible?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164659 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=164659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a bicycle race, Lionel gives Robert a 500 meter advantage. Lionel also agrees to start 15 minutes after Robert. If Lionel bikes at 17 km/h and Robert at 14 km/h how long will it take Lionel after he starts biking to overtake Robert?<BR>\n" );
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document.write( "Let's do it this way and then compare what you did<BR>\n" );
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document.write( "Let t = L's travel time<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t+.25) = R's travel time<BR>\n" );
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document.write( "A distance equation:<BR>\n" );
document.write( "L's dist - .5 km =  R's dist<BR>\n" );
document.write( "17t - .5 = 14(t+.25)<BR>\n" );
document.write( "17t - .5 = 14t + 3.5<BR>\n" );
document.write( "17t - 14t = 3.5 + .5<BR>\n" );
document.write( "3t = 4<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F3 ALIGN=MIDDLE  ALT=\"4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hr  or 1 hr 20 min for L to catch R<BR>\n" );
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document.write( "Check solution by finding the distance each traveled using decimals<BR>\n" );
document.write( "17 * 1.33 = 22.6 km<BR>\n" );
document.write( "14 * (1.33 +.25) = 22.1 mi<BR>\n" );
document.write( "a difference of .5 km<BR>\n" );
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document.write( "I think you had L starting before R instead of the other way around.<BR>\n" );
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