document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5211>Question 5211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've been working on word problems, but this one has me stumped. <BR>\n" );
document.write( "A car travels 120 miles. A second car; traveling 10 mph faster than the first car, makes the same trip in one hour less time. Find the speed of each car. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3274 by </B><A HREF=/tutors/aboutme.mpl?userid=glabow><B>glabow(165)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=glabow><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Always be careful and define the variables you are using.<BR>\n" );
document.write( "Let x = the speed of the first car<BR>\n" );
document.write( "Then x+10 = the speed of the second car<BR>\n" );
document.write( "Let t1 = the time the first car takes to travel 120 miles<BR>\n" );
document.write( "Then t2 = the time the second car takes to travel 120 miles<BR>\n" );
document.write( "We know that t1 = t2 + 1 (why?)\r<BR>\n" );
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document.write( "The equation for time of travel is <BR>\n" );
document.write( "     t = distance / speed\r<BR>\n" );
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document.write( "For the two cars we have the following equations\r<BR>\n" );
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document.write( "     t1 = 120 / x<BR>\n" );
document.write( "     t2 = 120 (x+10)<BR>\n" );
document.write( "Using t1 = t2 +1 we combine the two equations to<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120+%2F+%28x%2B10%29+%2B+1+=+120+%2F+x+ ALIGN=MIDDLE  ALT=\"+120+%2F+%28x%2B10%29+%2B+1+=+120+%2F+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is solved by the following steps<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+=+%28120+%2F+x%29+-+%28+120+%2F+%28x%2B10%29+%29 ALIGN=MIDDLE  ALT=\"+1+=+%28120+%2F+x%29+-+%28+120+%2F+%28x%2B10%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >     [rearranging terms]<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+=+%28%28120%29%28x%2B10%29+%2F+x%28x%2B10%29%29+-+%28%28120%29%28x%29+%2F+x%28x%2B10%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "           [multiply first term on right by (x+10) and second term on right by <BR>\n" );
document.write( "                                      x to get a common denominator]<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+=+%28120x+%2B+1200+-+120x%29+%2F+x%28x%2B10%29+ ALIGN=MIDDLE  ALT=\"+1+=+%28120x+%2B+1200+-+120x%29+%2F+x%28x%2B10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > [simplify and do subtraction]<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28x%2B10%29+=+1200+ ALIGN=MIDDLE  ALT=\"+x%28x%2B10%29+=+1200+\"   DISABLED_style= \"max-width:90%; height:auto;\" >                   [simplify and rearrange]<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+10x+-+1200+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+10x+-+1200+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >             [simplify and rearrange]<BR>\n" );
document.write( "This is most easily solved by factoring. The factors are numbers that multiply to -1200 and add up to 10. Numbers that satisfy these criteria are 40 and -30.<BR>\n" );
document.write( "So the equation becomes<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B40%29+%28x-30%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28x%2B40%29+%28x-30%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is true for x = -40 and x = 30. (why?)<BR>\n" );
document.write( "You cannot have a speed of -40. So x = 30.<BR>\n" );
document.write( "The speed of the first car is 30 miles/hr.<BR>\n" );
document.write( "The speed of the second car is 40 miles/hr.<BR>\n" );
document.write( "****Checking gives: the first car travels for 120/30 = 4 hours.<BR>\n" );
document.write( "                    the second car travels for 120/40 = 3 hours.<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
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