document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123733>Question 1123733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Karen and David set out from home at the same time. Karen cycles due north 20km/h and David due east at 15km/h. FInd<BR>\n" );
document.write( "a) how far apart they are in 1 hour <BR>\n" );
document.write( "b)after how many minutes they are 10km apart<BR>\n" );
document.write( "c) the bearing of Karen from David at any time  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #740200 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=740200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Karen and David set out from home at the same time.<BR>\n" );
document.write( " Karen cycles due north 20km/h and David due east at 15km/h. <BR>\n" );
document.write( "FInd<BR>\n" );
document.write( "a) how far apart they are in 1 hour<BR>\n" );
document.write( "their routes form a right triangle, the hypotenuse is the dist between them<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%5E2%2B15%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2820%5E2%2B15%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 25 km after 1 hr<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b)after how many minutes they are 10km apart<BR>\n" );
document.write( "Change the speeds to km/min<BR>\n" );
document.write( "20/60 = .33 km/min<BR>\n" );
document.write( "15/60 = .25 km/min<BR>\n" );
document.write( "let the t = time in min for them to be 10km apart<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28.33t%29%5E2+%2B+%28.25t%29%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"%28.33t%29%5E2+%2B+%28.25t%29%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.1111t%5E2+%2B+.0625t%5E2+=+100 ALIGN=MIDDLE  ALT=\".1111t%5E2+%2B+.0625t%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.1736t%5E2+=+100 ALIGN=MIDDLE  ALT=\".1736t%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+=+100%2F.1736 ALIGN=MIDDLE  ALT=\"t%5E2+=+100%2F.1736\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t^2 = 576<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28576%29 ALIGN=MIDDLE  ALT=\"sqrt%28576%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 24 min, they are 10 mi apart <BR>\n" );
document.write( ":<BR>\n" );
document.write( "c) the bearing of Karen from David at any time<BR>\n" );
document.write( "Find the angle (David's position) using the tangent tan(A) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F15 ALIGN=MIDDLE  ALT=\"20%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 53 degrees<BR>\n" );
document.write( "In relation to true north, 90-53 = 37 degrees,<BR>\n" );
document.write( "the Bearing then  360 - 37 = 323 degrees is Karen from David<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );