document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194181>Question 1194181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Phil leaves Northampton and walks north for an hour and a half. Don leaves Northampton<BR>\n" );
document.write( "at the same time and rides his bicycle south at a rate of 10 mph. Phil stops walking and<BR>\n" );
document.write( "Don continues to bike for another half an hour. At the end of the excursion, they find<BR>\n" );
document.write( "themselves 26 miles apart. What is Phil's rate? </SPAN>\n" );
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document.write( "The ultimate question here is \"What is Phil's rate?\" <BR>\n" );
document.write( "So we'll let x be the this unknown value\r<BR>\n" );
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document.write( "x = Phil's rate or speed in mph<BR>\n" );
document.write( "This is some positive real number.\r<BR>\n" );
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document.write( "Use the formula<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "to find this equation for Phil<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "d = x*1.5<BR>\n" );
document.write( "d = 1.5x\r<BR>\n" );
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document.write( "After 1.5 hours (aka an hour and a half), Phil has walked 1.5x miles.\r<BR>\n" );
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document.write( "Meanwhile, Don travels at a rate of 10 mph and started traveling south at the same time Phil went north.<BR>\n" );
document.write( "Don travels for the 1.5 hours mentioned, but an extra 1/2 = 0.5 an hour to get a total of 1.5+0.5 = 2 hours of travel.\r<BR>\n" );
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document.write( "Let's find how far Don traveled south:<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "d = 10*2<BR>\n" );
document.write( "d = 20<BR>\n" );
document.write( "Don traveled 20 miles south.\r<BR>\n" );
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document.write( "Add this onto the 1.5x miles Phil traveled north. Then set this to the 26 mile gap between the two people.<BR>\n" );
document.write( "It might help to draw out a vertical number line.<BR>\n" );
document.write( "1.5x+20 = 26<BR>\n" );
document.write( "1.5x = 26-20<BR>\n" );
document.write( "1.5x = 6<BR>\n" );
document.write( "x = 6/(1.5)<BR>\n" );
document.write( "x = 4\r<BR>\n" );
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document.write( "Answer: Phil's rate or speed is <font color=red>4 mph</font>.<BR>\n" );
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