document.write( "Question 970277: Colton went on a bike ride of 36 miles. He realized that if he had gone 3 mph faster, he would have arrived 6 hours sooner. How fast did he actually ride?
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Algebra.Com's Answer #592933 by ankor@dixie-net.com(22740)\"\" \"About 
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Colton went on a bike ride of 36 miles.
\n" ); document.write( " He realized that if he had gone 3 mph faster, he would have arrived 6 hours sooner.
\n" ); document.write( " How fast did he actually ride?
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\n" ); document.write( "let s = actual speed
\n" ); document.write( "then
\n" ); document.write( "(s+3) = the faster time speed
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\n" ); document.write( "Write a time equation, time = dist/speed
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\n" ); document.write( "Actual time - faster time = 6 hrs
\n" ); document.write( "\"36%2Fs\" - \"36%2F%28%28s%2B3%29%29\" = 6
\n" ); document.write( "multiply equation by s(s+3)
\n" ); document.write( "s(s+3)*\"36%2Fs\" - s(s+3)*\"36%2F%28%28s%2B3%29%29\" = 6s(s+3)
\n" ); document.write( "cancel the denominators
\n" ); document.write( "36(s+3) - 36s = 6s^2 + 18s
\n" ); document.write( "36s + 108 - 36s = 6s^2 + 18s
\n" ); document.write( "Combine as a quadratic equation on the right
\n" ); document.write( "0 = 6s^2 + 18s - 108
\n" ); document.write( "simplify, divide by 6
\n" ); document.write( "s^2 + 3s - 18 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(s + 6)(s - 3) = 0
\n" ); document.write( "the positive solution is all we want here
\n" ); document.write( "s = 3 mph his actual speed
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\n" ); document.write( "Check this find the actual time at each speed
\n" ); document.write( "36/3 = 12 hrs
\n" ); document.write( "36/6 = 6 hrs; 6 hrs faster\r
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