document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193910>Question 193910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sandy bicycled 45 miles going east from Cambridge and Janie, 70 miles. Janie averaged 5 miles per hour more than Sandy and her trip took 1/2 hour longer than Sandy's. How fast was each one traveling? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145586 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=145586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sandy bicycled 45 miles going east from Cambridge and Janie, 70 miles. Janie averaged 5 miles per hour more than Sandy and her trip took 1/2 hour longer than Sandy's. How fast was each one traveling?<BR>\n" );
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document.write( "I assume this means that Sandy traveled 45 miles and Janie traveled 70 miles.<BR>\n" );
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document.write( "let s = Sandy's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+5) = Janie's speed<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
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document.write( "Janie's travel time = Sandy's travel time + .5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70%2F%28%28s%2B5%29%29 ALIGN=MIDDLE  ALT=\"70%2F%28%28s%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2Fs ALIGN=MIDDLE  ALT=\"45%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5<BR>\n" );
document.write( "Multiply equation by s(s+5) to get rid of the denominators, results:<BR>\n" );
document.write( "70s = 45(s+5) + .5s(s+5)<BR>\n" );
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document.write( "70s = 45s + 225 + .5s^2 + 2.5s<BR>\n" );
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document.write( "0 = .5s^2 + 2.5s + 45s - 70s + 225<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( ".5s^2 - 22.5s + 225 = 0<BR>\n" );
document.write( "Multiply equation by 2 to eliminate the decimals<BR>\n" );
document.write( "s^2 - 45s + 450 = 0<BR>\n" );
document.write( "Factor<BR>\n" );
document.write( "(s - 15)(s - 30) = 0<BR>\n" );
document.write( "Two solutions for Sandy's speed<BR>\n" );
document.write( "s = 15<BR>\n" );
document.write( "and<BR>\n" );
document.write( "s = 30<BR>\n" );
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document.write( "Check using both solutions by finding the times;<BR>\n" );
document.write( "Sandy: 15 mph; Janie: 20 mph<BR>\n" );
document.write( "70/20 = 3.5 hr<BR>\n" );
document.write( "45/15 = 3.0 hr; a half hr difference<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Sandy: 30 mph; Janie: 35 mph<BR>\n" );
document.write( "70/35 = 2 hrs<BR>\n" );
document.write( "45/30 = 1.5 hrs; a half hr difference here too </SPAN>\n" );
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