document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150146>Question 1150146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The time it takes Karen to drive to work varies inversely with her speed and directly with the square root of the number of red stoplights she encounters. It takes Karen 45 minutes to get to work if she drives 35 mph and stops at 4 red stoplights. (a) Find the constant of proportionality, k. (b) How long does it take Karen to get to work if she drives 32 mph and stops at 3 red stoplights? Round your answer to the nearest tenth of a minute. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771557 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=771557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The time it takes Karen to drive to work varies inversely with her speed and directly with the square root of the number of red stoplights she encounters.<BR>\n" );
document.write( "let t = time to work (in hrs)<BR>\n" );
document.write( "let s = vehicle speed<BR>\n" );
document.write( "let r = no. of red lights<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28k%2Asqrt%28r%29%29%2Fs ALIGN=MIDDLE  ALT=\"t+=+%28k%2Asqrt%28r%29%29%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " It takes Karen 45 minutes to get to work if she drives 35 mph and stops at 4 red stoplights.<BR>\n" );
document.write( "Change 45 min = .75 hrs<BR>\n" );
document.write( " (a) Find the constant of proportionality, k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%2Asqrt%284%29%29%2F35 ALIGN=MIDDLE  ALT=\"%28k%2Asqrt%284%29%29%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .75<BR>\n" );
document.write( "2k = 35(.75)<BR>\n" );
document.write( "2k = 26.25<BR>\n" );
document.write( "k = 26.25/2<BR>\n" );
document.write( "k = 13.125<BR>\n" );
document.write( " (b) How long does it take Karen to get to work if she drives 32 mph and stops at 3 red stoplights?<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813.125%2Asqrt%283%29%29%2F32 ALIGN=MIDDLE  ALT=\"%2813.125%2Asqrt%283%29%29%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.538%2F32 ALIGN=MIDDLE  ALT=\"22.538%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = .7043 hrs<BR>\n" );
document.write( " Round your answer to the nearest tenth of a minute.<BR>\n" );
document.write( ".7043(60) = 42.3 minutes </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );