document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=941218>Question 941218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car travels 20km / h faster than a cyclist. The car takes one hour less than the cyclist to travel 150 km. Assuming the speed of the car is x km/h <BR>\n" );
document.write( "a) write down in terms of x expressions for the  time takrn by the car and the cyclist<BR>\n" );
document.write( "B) form a quadratic equation to connect these times<BR>\n" );
document.write( "C) SOLVE the equation to find the speed of the car and the cyclist </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #573776 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=573776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A car travels 20km / h faster than a cyclist.<BR>\n" );
document.write( " The car takes one hour less than the cyclist to travel 150 km.<BR>\n" );
document.write( " Assuming the speed of the car is x km/h<BR>\n" );
document.write( "a) write down in terms of x expressions for the time taken by the car and the cyclist<BR>\n" );
document.write( "Car time: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2Fx ALIGN=MIDDLE  ALT=\"150%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >; Cyclist: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F%28%28x-20%29%29 ALIGN=MIDDLE  ALT=\"150%2F%28%28x-20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "B) form a quadratic equation to connect these times<BR>\n" );
document.write( "  Cyclist time - car time = 1 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F%28%28x-20%29%29 ALIGN=MIDDLE  ALT=\"150%2F%28%28x-20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2Fx ALIGN=MIDDLE  ALT=\"150%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply equation by x(x-20)<BR>\n" );
document.write( "x(x-20)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F%28%28x-20%29%29 ALIGN=MIDDLE  ALT=\"150%2F%28%28x-20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - x(x-20)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2Fx ALIGN=MIDDLE  ALT=\"150%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x(x-20)<BR>\n" );
document.write( "Cancel the denominators and we have<BR>\n" );
document.write( "150x - 150(x-20) = x^2 - 20x<BR>\n" );
document.write( "150x - 150x + 3000 = x^2 - 20x<BR>\n" );
document.write( "combine to form a quadratic equation on right<BR>\n" );
document.write( "f(x) = x^2 - 20x - 3000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "C) SOLVE the equation to find the speed of the car and the cyclist<BR>\n" );
document.write( "x^2 - 20x - 3000 = 0<BR>\n" );
document.write( "Use the quadratic formula; a=1; b=-20; c=-3000<BR>\n" );
document.write( "I got a positive rounded off solution of:<BR>\n" );
document.write( "x = 65.68 is speed of the car<BR>\n" );
document.write( "and<BR>\n" );
document.write( "45.68 km/hr is the speed of the cyclist (20 km/hr less)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this by finding the actual time of each<BR>\n" );
document.write( "Cyclist: 150/45.68 = 3.28 hrs<BR>\n" );
document.write( "Car: 150/65.68 = 2.28 hrs,  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );