document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194434>Question 1194434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bicyclist bikes the 24 mi to a city averaging a certain speed. The return trip is made at a speed that is  4 mph slower. The total time for the round trip is  5 hr. Find the​ bicyclist's average speed on each part of the trip. </SPAN>\n" );
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document.write( "Get some good mental exercise by solving the problem informally.<br><BR>\n" );
document.write( "The distance is a whole number, the total time is a whole number, and the difference in speeds is a whole number.  So the two speeds are almost certain to be whole numbers.<br><BR>\n" );
document.write( "So look for two speeds that are whole numbers of miles per hour that differ by 4 and for which the total time going 24 miles and returning is 5 hours.  A little trial and error should quickly find speeds of 12 and 8 mph: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F12%2B24%2F8+=+2%2B3+=+5 ALIGN=MIDDLE  ALT=\"24%2F12%2B24%2F8+=+2%2B3+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "ANSWERS: 12mph going; 8mph returning<br><BR>\n" );
document.write( "With formal algebra....<br><BR>\n" );
document.write( "Let x be his speed going<BR>\n" );
document.write( "Then x-4 is his speed returning<br><BR>\n" );
document.write( "The total time for 24 miles each way is 5 hours:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2Fx%2B24%2F%28x-4%29=5 ALIGN=MIDDLE  ALT=\"24%2Fx%2B24%2F%28x-4%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply by the common denominator, x(x-4):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%28x-4%29%2B24%28x%29=5%28x%29%28x-4%29 ALIGN=MIDDLE  ALT=\"24%28x-4%29%2B24%28x%29=5%28x%29%28x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24x-96%2B24x=5x%5E2-20x ALIGN=MIDDLE  ALT=\"24x-96%2B24x=5x%5E2-20x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2-68x%2B96=0 ALIGN=MIDDLE  ALT=\"5x%5E2-68x%2B96=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-12%29%285x-8%29=0 ALIGN=MIDDLE  ALT=\"%28x-12%29%285x-8%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8%2F5 ALIGN=MIDDLE  ALT=\"x=8%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x=8/5 makes no sense, since it would make the return trip at a negative speed; so x=12.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "going: x=12mph<BR>\n" );
document.write( "returning: x-4=8mph<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );