document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=317526>Question 317526</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Car A is currently 80 km south of a perpendicular intersection with an east-west road. Car B is on the east-west road, 260 km west of the same intersection. Car A is travelling north at 80 km/h; Car B is travelling east at 100 km/h. Assuming that the cars will continue in a straight line with constant velocities, after 2 hours how fast is the distance between the two cars changing? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #227402 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=227402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's call A, the distance from the intersection to car A.<BR>\n" );
document.write( "Let's call B, the distance from the intersection to car B.<BR>\n" );
document.write( "The distance between the cars is D.<BR>\n" );
document.write( "A and B form a right triangle with D as the hypotenuse.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=A%5E2%2BB%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=A%5E2%2BB%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you differentiate with respect to time,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2D%2A%28dD%2Fdt%29=2A%2A%28dA%2Fdt%29%2B2B%2A%28dB%2Fdt%29 ALIGN=MIDDLE  ALT=\"2D%2A%28dD%2Fdt%29=2A%2A%28dA%2Fdt%29%2B2B%2A%28dB%2Fdt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "After 2 hours,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-80%2B80%2A2=80 ALIGN=MIDDLE  ALT=\"A=-80%2B80%2A2=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-260%2B100%2A2=-60 ALIGN=MIDDLE  ALT=\"B=-260%2B100%2A2=-60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdt=80 ALIGN=MIDDLE  ALT=\"dA%2Fdt=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dB%2Fdt=100 ALIGN=MIDDLE  ALT=\"dB%2Fdt=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=A%5E2%2BB%5E2=80%5E2%2B60%5E2=100%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=A%5E2%2BB%5E2=80%5E2%2B60%5E2=100%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=100 ALIGN=MIDDLE  ALT=\"D=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2D%2AdD%2Fdt=2A%2AdA%2Fdt%2B2%2AB%2AdB%2Fdt ALIGN=MIDDLE  ALT=\"2D%2AdD%2Fdt=2A%2AdA%2Fdt%2B2%2AB%2AdB%2Fdt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28100%29dD%2Fdt=2%2A80%2A80%2B2%28-60%29%2880%29 ALIGN=MIDDLE  ALT=\"2%28100%29dD%2Fdt=2%2A80%2A80%2B2%28-60%29%2880%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2AdD%2Fdt=2%2880%29%2880-60%29=3200 ALIGN=MIDDLE  ALT=\"200%2AdD%2Fdt=2%2880%29%2880-60%29=3200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dD%2Fdt=3200%2F200 ALIGN=MIDDLE  ALT=\"dD%2Fdt=3200%2F200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dD%2Fdt=16 ALIGN=MIDDLE  ALT=\"dD%2Fdt=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The only issue remaining is the sign of the rate of change.<BR>\n" );
document.write( "Distance A is growing while Distance B is diminishing (A is growing slower than B). <BR>\n" );
document.write( "Distance D is therefore diminishing. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28dD%2Fdt=-16%29 ALIGN=MIDDLE  ALT=\"highlight%28dD%2Fdt=-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > km/h\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );