document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=339836>Question 339836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cars are approaching an intersection. One is 3 miles South of the intersection and is moving at a constant speed of 40 mph. At the same time, the other car is 4 miles East of the intersection and is moving at a constant speed of 50 mph. Express the distance d between the cars as a function of time t. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #243522 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=243522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you basically have a right triangle formed by the movement of the cars, one from coming from the east and one coming from the south<BR>\n" );
document.write( "--<BR>\n" );
document.write( "let d=ditance between the cars.<BR>\n" );
document.write( "let x=distance from car from the east to the meeting point<BR>\n" );
document.write( "let y=distance from car from the south to the meeting point<BR>\n" );
document.write( "distance=speed*time; d=s*t<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Be%5D ALIGN=MIDDLE  ALT=\"D%5Be%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=Distance by car from east<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bs%5D ALIGN=MIDDLE  ALT=\"D%5Bs%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=Distance by car from south<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Be%5D ALIGN=MIDDLE  ALT=\"d%5Be%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=\"shrinking\" distance by car from east<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bs%5D ALIGN=MIDDLE  ALT=\"d%5Bs%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=\"shrinking\" distance by car from south<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bc%5D ALIGN=MIDDLE  ALT=\"D%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=Distance between cars<BR>\n" );
document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bc%5D ALIGN=MIDDLE  ALT=\"d%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=\"shrinking\" distance between cars<BR>\n" );
document.write( "--<BR>\n" );
document.write( "at t=0, one car is 4 miles east and the other car is 3 miles south, so the distance between them, by the pythagorean theorem:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bc%5D=sqrt%28x%5E2%2By%5E2%29=sqrt%283%5E2%2B4%5E2%29=5 ALIGN=MIDDLE  ALT=\"D%5Bc%5D=sqrt%28x%5E2%2By%5E2%29=sqrt%283%5E2%2B4%5E2%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "as time goes forward, the distances from the east and the south shrink toward their meeting point.<BR>\n" );
document.write( "car from the east travels a distance:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Be%5D=50%2At ALIGN=MIDDLE  ALT=\"D%5Be%5D=50%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > in general<BR>\n" );
document.write( "relative to the meeting point 4 miles away the distance shrinks<BR>\n" );
document.write( "as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Be%5D=4-50%2At ALIGN=MIDDLE  ALT=\"d%5Be%5D=4-50%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "car from the south travels a distance:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5Bs%5D=40%2At ALIGN=MIDDLE  ALT=\"D%5Bs%5D=40%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > in general<BR>\n" );
document.write( "relative to the meeting point 3 miles away the distance shrinks<BR>\n" );
document.write( "as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bs%5D=3-40%2At ALIGN=MIDDLE  ALT=\"d%5Bs%5D=3-40%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5Bc%5D=sqrt%28d%5E2%5Be%5D%2Bd%5E2%5Bs%5D%29=sqrt%28%284-50%2At%29%5E2%2B%283-40%2At%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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