document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164834>Question 1164834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car took 5 hours to travel from town A to town B. A bus took 9 hrs to travel the same route. both the car and bus started at the same time. if the speed of the car was 90km/h, how much faster did the bus need to travel in order to reach town B 1hr and 36 min earlier than the expected arrival time. if it could only increase it's speed after 3/5 of the journey? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789311 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.<BR>\n" );
document.write( "time = distance / rate<BR>\n" );
document.write( "rate = distance / time<BR>\n" );
document.write( "rate is the distance traveled in a specified period of time.<BR>\n" );
document.write( "that's the same as speed in this problem.\r<BR>\n" );
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document.write( "the car took 5  hours to travel from town A to town B.<BR>\n" );
document.write( "the speed of the car was 90 kilometers per hour.<BR>\n" );
document.write( "the distance was therefore 5 * 90 = 450 kilometers.\r<BR>\n" );
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document.write( "the bus took 9 hours to travel the same distance.<BR>\n" );
document.write( "the speed of the bus was therefore 450/9 = 50 kilometers per hour.\r<BR>\n" );
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document.write( "you want the bus to go from town A to town B 1 hour and 36 minutes earlier than its scheduled time.<BR>\n" );
document.write( "its scheduled time was 9 hours.<BR>\n" );
document.write( "1 hour and 36 minutes earlier is equal to 1 + 36/60 = 1.6 hours earlier.<BR>\n" );
document.write( "9 hour minus 1.6 hours is equal to 7.4 hours.<BR>\n" );
document.write( "the new scheduled time would need to be 7.4 hours rather than 9 hours so that the bus would go from town A to town B 1 hours and 36 minutes ahead of schedule.\r<BR>\n" );
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document.write( "to go from town A to town B in 7.4 hours, the bus would have to travel at a rate of 450 / 7.4 = 60.81081082 kilometers per hour rounded to 8 decimal digits.<BR>\n" );
document.write( "that would be an increase in speed of 10.81081082 kilometers per hour rouned to 8 decimal digits.\r<BR>\n" );
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document.write( "if the bus could only increase its speed after 3/5 of the journey was completed, then the bus could only increase speed after 3/5 * 450 = 270 kilometers were completed.<BR>\n" );
document.write( "that leaves 180 kilometers in which the bus could increase its speed.\r<BR>\n" );
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document.write( "270 kilometers at 50 kilometers takes 270/50 = 5.4 hours.<BR>\n" );
document.write( "to complete the whole trip in 7.4 hours, then the bus has 7.4 - 5.4 = 2 hours to complete 180 kilometers.<BR>\n" );
document.write( "to do that, the bus would need to travel 180 / 2 = 90 kilometers per hour.<BR>\n" );
document.write( "that would be an increase of 90 - 50 = 40 kilometers per hour.\r<BR>\n" );
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document.write( "to confirm these values are good. do the following.\r<BR>\n" );
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document.write( "450 kilometers completed in 7.4 hours equals a speed of 450 / 7.4 = 60.81081081 kilometers per hour for the whole trip.<BR>\n" );
document.write( "that's what we calculated before, so that's good.\r<BR>\n" );
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document.write( "450 kilometers at a speed of 50 kilometers per hour for the first 270 kilometers and at a speed of 90 kilometers per hour for the last 180 kilometers would take a total of 270 / 50 =  5.4 hours for the first 270 kilometers plus 180 / 90 = 2 hours for the last 180 kilometers for a total of 7.4 hours to cover the entire 450 kilometer distance.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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