document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=918210>Question 918210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a man travels equal distance at speeds v1 and v2 km/hr, his average speed is 4 km/hr. But when he travels at these speeds for equal times his average speed is 4.5 km/hr. Find the difference of two speeds </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557055 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=557055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a man travels equal distance at speeds v1 and v2 km/hr, his average speed is 4 km/hr.<BR>\n" );
document.write( " But when he travels at these speeds for equal times his average speed is 4.5 km/hr.<BR>\n" );
document.write( " Find the difference of two speeds<BR>\n" );
document.write( ";<BR>\n" );
document.write( "let 2d = the total distance<BR>\n" );
document.write( "\"When a man travels equal distance at speeds v1 and v2 km/hr, his average speed is 4 km/hr.\"<BR>\n" );
document.write( "A time equation; time = dist/speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28v1%29 ALIGN=MIDDLE  ALT=\"d%2F%28v1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28v2%29 ALIGN=MIDDLE  ALT=\"d%2F%28v2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282d%29%2F4 ALIGN=MIDDLE  ALT=\"%282d%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "reduce fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28v1%29 ALIGN=MIDDLE  ALT=\"d%2F%28v1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F%28v2%29 ALIGN=MIDDLE  ALT=\"d%2F%28v2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%2F2 ALIGN=MIDDLE  ALT=\"d%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide thru by d<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28v1%29 ALIGN=MIDDLE  ALT=\"1%2F%28v1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28v2%29 ALIGN=MIDDLE  ALT=\"1%2F%28v2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"when he travels at these speeds for equal times, his average speed is 4.5 km/hr\"<BR>\n" );
document.write( "let 2t = total time<BR>\n" );
document.write( "A distance equation; dist = speed * time<BR>\n" );
document.write( "v1*t + v2*t = 4.5(2t)<BR>\n" );
document.write( "v1*t + v2*t = 9t<BR>\n" );
document.write( "divide by t<BR>\n" );
document.write( "v1 + v2 = 9<BR>\n" );
document.write( "v2 = (9-v1)<BR>\n" );
document.write( "Replace v2 in the 1st simplified equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28v1%29 ALIGN=MIDDLE  ALT=\"1%2F%28v1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%289-v1%29 ALIGN=MIDDLE  ALT=\"1%2F%289-v1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 2(v1)(9-v1), cancel the denominators, you have<BR>\n" );
document.write( "2(9-v1) + 2(v1) = v1(9-v1)<BR>\n" );
document.write( "18 - 2(v1) + 2(v1) = 9(v1) - (v1)^2<BR>\n" );
document.write( "arrange to forma quadratic equation on the left<BR>\n" );
document.write( "(v1)^2 - 9(v1) + 18 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(v1 - 3)(v1 - 6) = 0<BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "v1 = 3; then v2 = 6<BR>\n" );
document.write( "v1 = 6; then v2 = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Obvious the difference is 3 in the two speeds<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "There should be an easier way to do this, but just can't come up with it this evening!\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );