document.write( "Question 63860This question is from textbook Intermediate Algebra with Applications
\n" ); document.write( ": The Tour De France is a bicycle race that begins in Dublin,Ireland, but is primarily a race through France.On each day,racers cover a certain distance depending on the steepness of terrian. Suppose that on one particular day, the racers must complete 210mi. One cyclist, traveling 10mph faster than a second cyclist, covers the distance in 2.4 hrs less time than the second cyclist. Find the rate of the first cyclist. \n" ); document.write( "
Algebra.Com's Answer #44574 by ankor@dixie-net.com(22740)\"\" \"About 
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the racers must complete 210 mi. One cyclist, traveling 10 mph faster than a second cyclist, covers the distance in 2.4 hrs less time than the second cyclist. Find the rate of the first cyclist.\r
\n" ); document.write( "\n" ); document.write( ":
\n" ); document.write( "Let s = the speed of the 1st cyclist
\n" ); document.write( "Let (s-10) = speed of the 2nd cyclist
\n" ); document.write( ":
\n" ); document.write( "Write a time equation: t = Dist/speed:
\n" ); document.write( ":
\n" ); document.write( "1st cyclist time + 2.4 hr = 2nd cyclist time
\n" ); document.write( " 210/s + 2.4 = 210/{s-10)
\n" ); document.write( ":
\n" ); document.write( "Mult the equation by s(s-10) to get rid of the denominators:
\n" ); document.write( " 210(s-10) + 2.4(s(s-10) = 210s
\n" ); document.write( "210s - 2100 + 2.4s^2 - 24s = 210s
\n" ); document.write( "2.4s^2 - 24s + 210s - 210s - 2100 = 0
\n" ); document.write( "2.4s^2 - 24s - 2100 = 0
\n" ); document.write( ":
\n" ); document.write( "Solve for s using the quadratic equation: a=2.4, b = -24; c = -2100
\n" ); document.write( ":
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "\"s+=+%28-%28-24%29+%2B-+sqrt%28+%28-24%29%5E2-+4%2A2.4%2A-2100+%29%29%2F%282%2A2.4%29+\"
\n" ); document.write( "\"s+=+%28%2B24+%2B-+sqrt%28576+-+%28-20160%29%29%29%2F%284.8%29+\"
\n" ); document.write( "\"s+=+%2824+%2B-+sqrt%28576+%2B+20160%29%29%2F%284.8%29+\"
\n" ); document.write( "Do the math and you should get a positive solution of:
\n" ); document.write( "s = + 35 mph is the speed of the 1st cyclist
\n" ); document.write( ":
\n" ); document.write( "Check solution using the time difference:
\n" ); document.write( "210/35 - 210/25 = 2.4 hrs\r
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