document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167191>Question 1167191</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A trucker drove 140 miles to make a delivery and returned home on the same route. Because of foggy conditions, his average speed on the return trip was 15 mph less than his average speed going. If the return trip took 3 hours longer, how fast did he drive in each direction? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #791789 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=791789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let the speed going be x and the speed going be x-15.<br><BR>\n" );
document.write( "The time going is then 140/x and the time returning is 140/(x-15).<br><BR>\n" );
document.write( "The time returning is 3 hours more than the time going:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140%2F%28x-15%29+=+140%2Fx%2B3 ALIGN=MIDDLE  ALT=\"140%2F%28x-15%29+=+140%2Fx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140%2F%28x-15%29+=+%28140%2B3x%29%2Fx ALIGN=MIDDLE  ALT=\"140%2F%28x-15%29+=+%28140%2B3x%29%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140x+=+%28140%2B3x%29%28x-15%29 ALIGN=MIDDLE  ALT=\"140x+=+%28140%2B3x%29%28x-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140x+=+3x%5E2%2B95x-2100 ALIGN=MIDDLE  ALT=\"140x+=+3x%5E2%2B95x-2100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-45x-2100+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2-45x-2100+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-15x-700+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-15x-700+=+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=%28x-35%29%28x%2B20%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-35%29%28x%2B20%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+=+35 ALIGN=MIDDLE  ALT=\"x+=+35\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-20 ALIGN=MIDDLE  ALT=\"x+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Clearly the negative solution makes no sense in the problem....<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "speed going = x = 35mph<BR>\n" );
document.write( "speed returning = x-15 = 20mph<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "time going = 140/35 = 4 hours<BR>\n" );
document.write( "time returning = 140/20 = 7 hours = 3 hours more than time going<br><BR>\n" );
document.write( "That's a formal algebraic solution, which involves a lot of work -- especially factoring the quadratic into two linear factors.<br><BR>\n" );
document.write( "If a formal algebraic solution is not required, a little mental arithmetic will find the answer much faster and with much less effort.  Simply look for combinations of hours and miles per hour that make 140 miles.<br><BR>\n" );
document.write( "Two easy combinations that satisfy all the conditions of the problem are<BR>\n" );
document.write( "(1) 4*35 = 140 --> 4 hours at 35mph<BR>\n" );
document.write( "(2) 7*20 = 140 --> 7 hours at 20mph<br><BR>\n" );
document.write( " </SPAN>\n" );
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