document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636832>Question 636832</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The distance between city A and B is 90 kilometers. At the same time, a car and a motorcycle left from city A to city B. The motorcycle drove at a constant speed the entire drive and the car passed 1/3 of the drive 30 kilometers per hour faster than the motorcycle's speed, stopped for half an hour, and then continued the drive at a speed 20% slower than the speed driven in the first 1/3 of the drive. The car arrived 15 minutes before the motorcycle to city B (they drove the same distance). What was the speed of the motorcycle?\r<BR>\n" );
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document.write( "This is supposed to be easy, I just keep messing up somewhere.<BR>\n" );
document.write( "I know Distance=Speed*Time<BR>\n" );
document.write( "The motorcycle's speed is x, and the time is 90/x (because the distance is 90)<BR>\n" );
document.write( "The car's speed is x+30, and the time is 30/x+30 (because 1/3 of 90 is 30)<BR>\n" );
document.write( "Then the speed is .80(x+30) and the time is 60/.8x+24 (the remaining distance being 60 km)<BR>\n" );
document.write( "but the car stopped for half an hour, and then arrived 15 minutes before the motorcycle, so I only add 1/4 of an hour to the time in the second equation.. <BR>\n" );
document.write( "After this step I keep getting stuck... Could you please help me finish?<BR>\n" );
document.write( "Thanks so much! I don't know what I would do without your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401299 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=401299\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The distance between city A and B is 90 kilometers.<BR>\n" );
document.write( " At the same time, a car and a motorcycle left from city A to city B. <BR>\n" );
document.write( "The motorcycle drove at a constant speed the entire drive and the car passed<BR>\n" );
document.write( " 1/3 of the drive 30 kilometers per hour faster than the motorcycle's speed,<BR>\n" );
document.write( " stopped for half an hour, and then continued the drive at a speed 20% slower<BR>\n" );
document.write( " than the speed driven in the first 1/3 of the drive. <BR>\n" );
document.write( "The car arrived 15 minutes before the motorcycle to city B (they drove the same distance). <BR>\n" );
document.write( "What was the speed of the motorcycle?<BR>\n" );
document.write( "This is supposed to be easy, I just keep messing up somewhere.<BR>\n" );
document.write( "I know Distance=Speed*Time<BR>\n" );
document.write( "The motorcycle's speed is x, and the time is 90/x (because the distance is 90)<BR>\n" );
document.write( "The car's speed is x+30, and the time is 30/x+30 (because 1/3 of 90 is 30)<BR>\n" );
document.write( "Then the speed is .80(x+30) and the time is 60/.8x+24 (the remaining distance being 60 km)<BR>\n" );
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document.write( "From what I see here, you have a time equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F%28x%2B30%29 ALIGN=MIDDLE  ALT=\"30%2F%28x%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28.8%28x%2B30%29%29 ALIGN=MIDDLE  ALT=\"60%2F%28.8%28x%2B30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2Fx ALIGN=MIDDLE  ALT=\"90%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - .25<BR>\n" );
document.write( "we can simplify the 2nd fraction, divide .8 into 60 and we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F%28x%2B30%29 ALIGN=MIDDLE  ALT=\"30%2F%28x%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75%2F%28%28x%2B30%29%29 ALIGN=MIDDLE  ALT=\"75%2F%28%28x%2B30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + .5 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2Fx ALIGN=MIDDLE  ALT=\"90%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - .25<BR>\n" );
document.write( "subtract .5 from both sides, add fractions with same denominator and we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=105%2F%28x%2B30%29 ALIGN=MIDDLE  ALT=\"105%2F%28x%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%2Fx ALIGN=MIDDLE  ALT=\"90%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - .75<BR>\n" );
document.write( "Multiply by x(x+30) to clear denominators, results:<BR>\n" );
document.write( "105x = 90(x+30) - .75x(x+30)<BR>\n" );
document.write( "105x = 90x + 2700 - .75x^2 - 22.5x<BR>\n" );
document.write( "Arrange as a quadratic equation on the left<BR>\n" );
document.write( ".75x^2 + 22.5x - 90x + 105x - 2700 = 0<BR>\n" );
document.write( ".75x^2 + 37.5x - 2700 = 0<BR>\n" );
document.write( "Simplify, divide by .75. results<BR>\n" );
document.write( "x^2 + 50x - 3600 = 0<BR>\n" );
document.write( "This will factor to<BR>\n" );
document.write( "(x+90)(x-40) = 0<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "x = 40 mph is the motorcycle speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this out in the original time equation </SPAN>\n" );
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