document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196996>Question 1196996</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Two cyclists start from the same point and ride in opposite directions. One cyclist rides twice as fast as the other. In 3 hr, they are 126 mi apart. Find the rate of each cyclist. \r<BR>\n" );
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document.write( "Slower cyclist _______=MPH<BR>\n" );
document.write( "Faster cyclist _______=MPH </SPAN>\n" );
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document.write( "x = speed of the slower cyclist<BR>\n" );
document.write( "2x = speed of the faster cyclist (traveling twice as fast)<BR>\n" );
document.write( "speeds are in miles per hour (mph)<BR>\n" );
document.write( "The variable x is a placeholder for some positive real number\r<BR>\n" );
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document.write( "After 3 hours, we have these respective distances traveled<BR>\n" );
document.write( "slower = 3x<BR>\n" );
document.write( "faster = 3*2x = 6x<BR>\n" );
document.write( "I used the formula distance = rate*time\r<BR>\n" );
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document.write( "These two distances must add to the 126 miles. <BR>\n" );
document.write( "You could draw out a diagram like shown below to help visualize what's happening.<BR>\n" );
document.write( "Once you get used to problems like this, the diagram becomes optional in my opinion. But it's helpful to draw out a diagram whenever you get stuck.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://i.imgur.com/x2mEFYh.png\"><BR>\n" );
document.write( "They both start at point A<BR>\n" );
document.write( "The slower cyclist goes to point B, traveling 3x miles<BR>\n" );
document.write( "The faster cyclist goes to point C, traveling 6x miles<BR>\n" );
document.write( "The distance from B to C is 126 miles, aka 3x+6x\r<BR>\n" );
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document.write( "(slower cyclist's distance) + (faster cyclist's distance) = 126<BR>\n" );
document.write( "(3x)+(6x) = 126<BR>\n" );
document.write( "9x = 126<BR>\n" );
document.write( "x = 126/9<BR>\n" );
document.write( "x = 14<BR>\n" );
document.write( "which is the slower cyclist's speed<BR>\n" );
document.write( "and 2x = 2*14 = 28 mph is the faster cyclist's speed\r<BR>\n" );
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document.write( "The slower cyclist travels for 3*14 = 42 miles<BR>\n" );
document.write( "The faster cyclist travels for 3*28 = 84 miles<BR>\n" );
document.write( "Note: the faster cyclist travels twice as far\r<BR>\n" );
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document.write( "The total distance is 42+84 = 126 miles which helps fully verify our answers.\r<BR>\n" );
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document.write( "Answer:  <BR>\n" );
document.write( "Slower cyclist = <font color=red>14</font> mph<BR>\n" );
document.write( "Faster cyclist = <font color=red>28</font> mph<BR>\n" );
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