document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204036>Question 1204036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> steve McPoke left home on his bivcycle at 8 am. traveling at 18 km/h. at 10 am, steve's brother set out after him on a motorcycle , folowing the same route. The motorcycle traveled at 54 km/h. How long had steve traveled when his brother overtok him? </SPAN>\n" );
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document.write( "n = number of hours that elapse after 8 am.\r<BR>\n" );
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document.write( "Steve travels for n hours<BR>\n" );
document.write( "Steve travels 18n kilometers because distance = rate*time.\r<BR>\n" );
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document.write( "Steve's brother travels n-2 hours because he's on the road for two fewer hours. Eg: Steve is on the road for 5 hours, while his brother is on the road for 3 hours.\r<BR>\n" );
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document.write( "Steve's brother travels 54(n-2) kilometers.\r<BR>\n" );
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document.write( "Steve's brother catches up to Steve when the two men travel the same distance.<BR>\n" );
document.write( "18n = 54(n-2)<BR>\n" );
document.write( "18n = 54n-108<BR>\n" );
document.write( "18n-54n = -108<BR>\n" );
document.write( "-36n = -108<BR>\n" );
document.write( "n = -108/(-36)<BR>\n" );
document.write( "n = 3<BR>\n" );
document.write( "Steve's brother catches up with Steve 3 hours after 8 am.<BR>\n" );
document.write( "The two brothers meet up at 11 am because 8 am + 3 hrs = 11 am.\r<BR>\n" );
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document.write( "Another method\r<BR>\n" );
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document.write( "m = number of hours Steve's brother is on the road.<BR>\n" );
document.write( "m+2 = number of hours Steve is on the road, since he gets a 2 hour head start.\r<BR>\n" );
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document.write( "18(m+2) = distance Steve travels<BR>\n" );
document.write( "54m = distance Steve's brother travels\r<BR>\n" );
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document.write( "18(m+2) = 54m<BR>\n" );
document.write( "18m+36 = 54m<BR>\n" );
document.write( "36 = 54m-18m<BR>\n" );
document.write( "36 = 36m<BR>\n" );
document.write( "36m = 36<BR>\n" );
document.write( "m = 36/36<BR>\n" );
document.write( "m = 1<BR>\n" );
document.write( "Steve's brother is on the road for 1 hour.<BR>\n" );
document.write( "The two brothers meet up at 11 am since 10 am + 1 hr = 11 am\r<BR>\n" );
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document.write( "Steve is on the road for m+2 = 1+2 = 3 hours when his brother passes him.\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>3 hours</font><BR>\n" );
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