document.write( "Question 63833: A cyclist bikes x distance at 10 mph and returns over the same path at 8 mph. What is the cyclists average rate for the round trip in miles per hour. \n" ); document.write( "
Algebra.Com's Answer #44498 by Edwin McCravy(20059)\"\" \"About 
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document.write( "A cyclist bikes x distance at 10 mph and returns\r\n" );
document.write( "over the same path at 8 mph. What is the cyclist's \r\n" );
document.write( "average rate for the round trip in miles per hour.\r\n" );
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document.write( "First, I'll tell you what it is NOT. It it NOT the \r\n" );
document.write( "average of the two rates, or it is NOT 9 mph, but \r\n" );
document.write( "a little bit less.\r\n" );
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document.write( "Since she travels a distance of x miles at 10 mph \r\n" );
document.write( "then, using TIME = DISTANCE/RATE, it took her x/10 \r\n" );
document.write( "hours to travel the x miles going.\r\n" );
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document.write( "Since she then travels a distance of x miles at \r\n" );
document.write( "8 mph then, using TIME = DISTANCE/RATE,  it took \r\n" );
document.write( "her x/8 hours to travel the x miles returning.\r\n" );
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document.write( "Her total distance was 2x miles and her total time \r\n" );
document.write( "was x/10 + x/8. To simplify that we must get an \r\n" );
document.write( "LCD of 40\r\n" );
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document.write( "x/10 + x/8 = 4x/40 + 5x/40 = 9x/40\r\n" );
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document.write( "AVERAGE RATE =\r\n" );
document.write( "  (TOTAL DISTANCE TRAVELED)÷(TOTAL TIME TRAVELED)\r\n" );
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document.write( "so  \r\n" );
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document.write( "AVERAGE RATE = (2x)÷(9x/40) = (2x)·[40/(9x)] = \r\n" );
document.write( "(80x)/(9x) = 80/9 = 8 8/9 mph, which is a little \r\n" );
document.write( "less than the average of her two speeds. \r\n" );
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document.write( "Edwin
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