document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189896>Question 1189896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cyclists start at the same point and travel in opposite directions. <BR>\n" );
document.write( "One cyclist travels 3 km faster than the other. <BR>\n" );
document.write( "If the two cyclists are 90 kilometers apart after 2 hours, what is the rate of each cyclist? </SPAN>\n" );
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document.write( "x = speed of the slower cyclist<BR>\n" );
document.write( "x+3 = speed of the faster cyclist (since he or she travels 3 km/hr faster)\r<BR>\n" );
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document.write( "We'll use this formula<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "often abbreviated as<BR>\n" );
document.write( "d = r*t\r<BR>\n" );
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document.write( "For the slower cyclist, we have this equation<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "d = x*t\r<BR>\n" );
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document.write( "Meanwhile, the faster cyclist has this distance equation<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "d = (x+3)*t\r<BR>\n" );
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document.write( "So x*t and (x+3)*t represents how far the slower and faster cyclist traveled in that order.\r<BR>\n" );
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document.write( "Since they start at the same point, and travel in opposite directions, this means adding the two said expressions will yield the total distance they are apart.\r<BR>\n" );
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document.write( "distance between cyclists = x*t + (x+3)*t\r<BR>\n" );
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document.write( "Set that equal to the desired 90 km, and also plug in t = 2 to represent 2 hours. Solve for x.\r<BR>\n" );
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document.write( "x*t + (x+3)*t = 90<BR>\n" );
document.write( "x*2 + (x+3)*2 = 90<BR>\n" );
document.write( "2x + 2x+6 = 90<BR>\n" );
document.write( "4x+6 = 90<BR>\n" );
document.write( "4x = 90-6<BR>\n" );
document.write( "4x = 84<BR>\n" );
document.write( "x = 84/4<BR>\n" );
document.write( "x = 21\r<BR>\n" );
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document.write( "This x value leads to<BR>\n" );
document.write( "x+3 = 21+3 = 24\r<BR>\n" );
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document.write( "The slower cyclist travels at a speed of 21 km/hr<BR>\n" );
document.write( "After 2 hours, s/he travels x*t = 21*2 = 42 km\r<BR>\n" );
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document.write( "The faster cyclist travels at a speed of 24 km/hr<BR>\n" );
document.write( "After 2 hours, s/he travels (x+3)*t = 24*2 = 48 km<BR>\n" );
document.write( "The sum of their distances is 42+48 = 90 km<BR>\n" );
document.write( "This confirms our answers.\r<BR>\n" );
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document.write( "-----------------------------------------------\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "Slower cyclist speed = 21 km/hr<BR>\n" );
document.write( "Faster cyclist speed = 24 km/hr<BR>\n" );
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