document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939969>Question 939969</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A salesman drives from Ajax to Barrington, a distance of 140 mi, at a steady speed. He then increases his speed by 15 mi/h to drive the 180 mi from Barrington to Collins. If the second leg of his trip took 4 min more time than the first leg, how fast was he driving between Ajax and Barrington?<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 #572836 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=572836\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A salesman drives from Ajax to Barrington, a distance of 140 mi, at a steady speed.<BR>\n" );
document.write( " He then increases his speed by 15 mi/h to drive the 180 mi from Barrington to Collins.<BR>\n" );
document.write( " If the second leg of his trip took 4 min more time than the first leg,how fast was he driving between Ajax and Barrington?<BR>\n" );
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document.write( "let s = his original speed<BR>\n" );
document.write( "(s+15) = his increased speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140%2Fs ALIGN=MIDDLE  ALT=\"140%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > time from Aj to Bar<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F%28%28s%2B15%29%29 ALIGN=MIDDLE  ALT=\"180%2F%28%28s%2B15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = time from Bar to Col<BR>\n" );
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document.write( "Bar/Col time - Aj/Bar time = 4 min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F%28%28s%2B15%29%29 ALIGN=MIDDLE  ALT=\"180%2F%28%28s%2B15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140%2Fs ALIGN=MIDDLE  ALT=\"140%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F60 ALIGN=MIDDLE  ALT=\"4%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > (we have to convert 4 min to hrs)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%2F%28%28s%2B15%29%29 ALIGN=MIDDLE  ALT=\"180%2F%28%28s%2B15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140%2Fs ALIGN=MIDDLE  ALT=\"140%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F15 ALIGN=MIDDLE  ALT=\"1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > (reduce the fraction)<BR>\n" );
document.write( "multiply equation by 15s(s+15), cancel the denominators and you have<BR>\n" );
document.write( "15s(180) - 15(s+15)(140) = s(s+15)<BR>\n" );
document.write( "2700s - (15s+225)(140) = s^2 + 15s<BR>\n" );
document.write( "2700s - 2100s - 31500 = s^2 + 15s<BR>\n" );
document.write( "600s - 31500 = s^2 + 15s<BR>\n" );
document.write( "Combine on the right to form a quadratic equation<BR>\n" );
document.write( "0 = s^2 + 15s - 600s + 31500<BR>\n" );
document.write( "0 = s^2 - 585s + 31500<BR>\n" );
document.write( "you can use the quadratic formula here a=1; b=-585; c=31500. however this will factor<BR>\n" );
document.write( "(s-525)(s-60) = 0<BR>\n" );
document.write( "s = 525, not reasonable<BR>\n" );
document.write( "s = 60 mph, his speed from Aj to Bar<BR>\n" );
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document.write( "See if that checks out; (Bar/Col speed is 15 mph more or 75 mph)<BR>\n" );
document.write( "180/75 = 2.40 hrs<BR>\n" );
document.write( "140/60 = 2.3333 hrs<BR>\n" );
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document.write( "differs by .067 hrs, convert to min; .067(60) ~ 4.0 min\r<BR>\n" );
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