document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205398>Question 1205398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train normally travels between two stations at v km/h. If its average speed is increased in the ratio m:n, will it take more or less time?<BR>\n" );
document.write( "In what ratio is the time changed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842172 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=842172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the speed is increased, then it will take less time.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "v is the original speed.<BR>\n" );
document.write( "it is increased by the ratio m:n<BR>\n" );
document.write( "if it is increased, then m must be greater than v.\r<BR>\n" );
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document.write( "increase in a ratio means to multiply the original value by by a fraction where the numerator is greater than the denominator.\r<BR>\n" );
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document.write( "v * m/n is greater than v.\r<BR>\n" );
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document.write( "if the speed is increased, the time to get to the destination will be less.\r<BR>\n" );
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document.write( "note that these problems use the general formula of r * t = d.<BR>\n" );
document.write( "r is the speed of the vehicle.<BR>\n" );
document.write( "t is the time it takes the vehicle to get to the destination.<BR>\n" );
document.write( "d is the distance to get to the destination.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "r*t=d becomes 5*5=25 when r = 5 and t = 5.<BR>\n" );
document.write( "the rate of the vehicle is 5 kilometers per hour.<BR>\n" );
document.write( "the time it takes to the destination is 5 hours.<BR>\n" );
document.write( "the distance if 5 kilometers per hour * 5 hours = 25 kilometers.\r<BR>\n" );
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document.write( "if you multiply r by 5/2, then r = 5 * 5/2 = 25/2 = 12.5<BR>\n" );
document.write( "the new speed of the vehicle becomes 12.5 kilometers per hour.\r<BR>\n" );
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document.write( "rt=d becomes 12.5 * t = 25<BR>\n" );
document.write( "solve for t to get t = 25/12.5 = 2\r<BR>\n" );
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document.write( "speed was increased, therefore time was decreased.\r<BR>\n" );
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document.write( "in what ratio was the time changed?\r<BR>\n" );
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document.write( "see below.\r<BR>\n" );
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document.write( "the formula is R * T = D<BR>\n" );
document.write( "when you increase the rate by m/n, then the formula becomes R * n/m * T = D<BR>\n" );
document.write( "if you divide both sides of the formula by R, you get m/n * T = D/R<BR>\n" );
document.write( "if you multiply both sides of the equation by n/m, you get T = D/R * n/m<BR>\n" );
document.write( "so your answer for in what ratio is the time changed should be n/m.<BR>\n" );
document.write( "in my example, the original value of t was 5.<BR>\n" );
document.write( "after multiplying the rate by 5/2, t was then 2.<BR>\n" );
document.write( "so t must have been multiplied by 2/5 because 5 * 2/5 = 2<BR>\n" );
document.write( "if 5/2 was m/n, then 2/5 must be n/m.\r<BR>\n" );
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document.write( "let me know if if your have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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