document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034986>Question 1034986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A salesman drives from Ajax to Barrington, a distance of 114 mi, at a steady speed. He then increases his speed by 14 mi/h to drive the 141 mi from Barrington to Collins. If the second leg of his trip took 3 min more time than the first leg, how fast was he driving between Ajax and Barrington? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649637 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=649637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A salesman drives from Ajax to Barrington, a distance of 114 mi, at a steady speed.<BR>\n" );
document.write( " He then increases his speed by 14 mi/h to drive the 141 mi from Barrington to Collins.<BR>\n" );
document.write( " If the second leg of his trip took 3 min more time than the first leg, how fast was he driving between Ajax and Barrington?<BR>\n" );
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document.write( "A-------114------B--------141---------C<BR>\n" );
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document.write( "Let s = his speed from A to B<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+14) = his speed from B to C<BR>\n" );
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document.write( "Change 3 min to hrs: 3/60 reduces to 1/20<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( "AB time - BC time = 3 min<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=141%2F%28%28s%2B14%29%29 ALIGN=MIDDLE  ALT=\"141%2F%28%28s%2B14%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=114%2Fs ALIGN=MIDDLE  ALT=\"114%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F20 ALIGN=MIDDLE  ALT=\"1%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply equation by 20s(s+14), cancel the denominators and you have<BR>\n" );
document.write( "20s(141) - 20(s+14)(114) = s(s+14)<BR>\n" );
document.write( "20s(141) - 2280(s+14) = s(s+14)<BR>\n" );
document.write( "2820s - 2280s - 31920 = s^2 + 14s<BR>\n" );
document.write( "540s - 31920 = s^2 + 14s<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "0 = s^2 + 14s - 540s + 31920<BR>\n" );
document.write( "s^2 - 526s + 31920 = 0<BR>\n" );
document.write( "The quadratic formula; a=1; b=-426; c=31920; reveals two solutions<BR>\n" );
document.write( "s = 456, not reasonable in a car<BR>\n" );
document.write( "and<BR>\n" );
document.write( "s = 70 mph is the speed from A to B<BR>\n" );
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document.write( "See if that checks out, find the actual time for each part (BC is 84mph)<BR>\n" );
document.write( "141/84 = 1.67857 hrs<BR>\n" );
document.write( "114/70 = 1.62857 hrs<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "difference: .05 hrs;  which is 3 min.  (3/60 = .05)<BR>\n" );
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document.write( "Hey, did this make sense to you? I like to know if I am explaining this sufficiently.  Thanks. CK </SPAN>\n" );
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