document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=293835>Question 293835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man walks a certain distance at a certain speed. Had he walked 1/2 km / hr faster, he would have taken one hour less. But if he had walked 1 km /hour slower, he would have taken 3 hours longer. the distance travelled by him is ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212055 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=212055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A man walks a certain distance at a certain speed.<BR>\n" );
document.write( " Had he walked 1/2 km / hr faster, he would have taken one hour less.<BR>\n" );
document.write( " But if he had walked 1 km /hour slower, he would have taken 3 hours longer.<BR>\n" );
document.write( " The distance traveled by him is:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let r = the rate the man walked<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(r+.5) = 1 hr less rate<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(r-1) = 3 hr more rate<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let t = time he actually walked<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t-1) = time at the faster rate<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(t+3) = time at the slower rate<BR>\n" );
document.write( ":<BR>\n" );
document.write( "distance for all three situations is the same (dist = rate * time):<BR>\n" );
document.write( ";<BR>\n" );
document.write( "actual dist = faster time dist<BR>\n" );
document.write( "rt = (r+.5)(t-1)<BR>\n" );
document.write( "rt = rt - r + .5t - .5<BR>\n" );
document.write( "rt - rt + r - .5t = -.5<BR>\n" );
document.write( "r - .5t = -.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "actual dist = slower time dist<BR>\n" );
document.write( "rt = (r-1)(t+3)<BR>\n" );
document.write( "rt = rt + 3r -t - 3<BR>\n" );
document.write( "rt - rt - 3r + t = -3<BR>\n" );
document.write( "-3r + t = -3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "multiply the 1st equation by 2 and add to the above equation<BR>\n" );
document.write( "2r - t = -1<BR>\n" );
document.write( "-3r + t = -3<BR>\n" );
document.write( "---------------eliminates t<BR>\n" );
document.write( "-r = -4<BR>\n" );
document.write( "r = 4 km/h is the actual walking rate<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find t using: r -.5t = -.5<BR>\n" );
document.write( "4 - .5t = -.5<BR>\n" );
document.write( "-.5t = -.5 - 4<BR>\n" );
document.write( "-.5t = - 4.5<BR>\n" );
document.write( "Multiply eq by -2<BR>\n" );
document.write( "t = 9 hrs actual time<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Dist = r*t<BR>\n" );
document.write( "4 * 9 = 36 km<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "see if this is true; find the time of each scenario<BR>\n" );
document.write( "36/4.5 = 8 hrs (1h less)<BR>\n" );
document.write( "36/3 = 12 hrs (3hr more)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );