document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949647>Question 949647</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A train running between City A and City B arrives at its destination 10minutes late when it goes at 40kms.per hour. And 16minutes late when it goes at 30kms. per hour. What is the distance between two cities? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579784 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=579784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you either want to convert minutes to hours or hours to minutes.\r<BR>\n" );
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document.write( "we'll try converting minutes to hours.<BR>\n" );
document.write( "you could just as easily solve the problem by converting hours to minutes.<BR>\n" );
document.write( "the key is that you need to be dealing with consistent units in order to solve the problem correctly.\r<BR>\n" );
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document.write( "10 minutes = 1/6 of an hour.\r<BR>\n" );
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document.write( "16 minutes = 4/15 of an hour.\r<BR>\n" );
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document.write( "the general equation to use is r*t = d<BR>\n" );
document.write( "r = rate of speed in kilometers per hour.<BR>\n" );
document.write( "t = time in hours.<BR>\n" );
document.write( "d = distance in kilometers.\r<BR>\n" );
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document.write( "you have 2 equations to work with.\r<BR>\n" );
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document.write( "40*(t+1/6) = d<BR>\n" );
document.write( "30*(t+4/15) = d\r<BR>\n" );
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document.write( "if you replace d in the first equation with its equivalent value from the second equation, you will get:\r<BR>\n" );
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document.write( "40*(t+1/6) = 30*(t+4/15)\r<BR>\n" );
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document.write( "simplify by performing the indicated operations to get:\r<BR>\n" );
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document.write( "40*t + 40/6 = 30*t + 120/15\r<BR>\n" );
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document.write( "subtract 30*t from both sides of the equation and subtract 40/6 from both sides of the equation to get:\r<BR>\n" );
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document.write( "40*t - 30*t= 120/15 - 40/6\r<BR>\n" );
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document.write( "the least common denominator on the right looks like it's 30, so we'll convert those fractions to fractions with a denominator of 30.\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "40*t - 30*t = 240/30 - 200/30\r<BR>\n" );
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document.write( "simplify to get 10*t = 40/30\r<BR>\n" );
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document.write( "divide both sides of that equation by 10 and you get:\r<BR>\n" );
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document.write( "t = 40/300 = 4/30 = 2/15 hours.\r<BR>\n" );
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document.write( "now that you know the value of t, you can use that to solve for the distance.\r<BR>\n" );
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document.write( "first equation of 40*(t+1/6) = d becomes 40*(2/15+1/6) = d which becomes 40*(4/30 + 5/30) = d which becomes 40*9/30 = d which becomes 360/30 = d which becomes 36/3 = d which becomes 12 = d.\r<BR>\n" );
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document.write( "second equation of 30*(t+4/15) = d becomes 30*(2/15+4/15) = d which becomes 30*(6/15) = d which becomes 180/15 = d which becomes 12 = d.\r<BR>\n" );
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document.write( "d = 12 in both equation which confirms the value of d is good since d had to be the same in both equations.\r<BR>\n" );
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document.write( "the distance between the 2 cities is 12 kilometers.\r<BR>\n" );
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document.write( "that's your solution and you can stop here if you wish.\r<BR>\n" );
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document.write( "you can go one step further if you like, but you don't have to.\r<BR>\n" );
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document.write( "i'll go the one step further just to show you.\r<BR>\n" );
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document.write( "now that you know the distance, you can solve for how fast the train should have been going to be on time.\r<BR>\n" );
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document.write( "r*t = d is the general equation to use.\r<BR>\n" );
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document.write( "you have t = 2/15 and d = 12.<BR>\n" );
document.write( "solve for r to get r = d/t = 12/(2/15) which is equal to 12*(15/2) which is equal to 6*15 which is equal to 90 kilometers per hour.\r<BR>\n" );
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document.write( "the train needed to be traveling at 90 kilometers per hour to be on time.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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