document.write( "Question 1064928: The distance between two points And B is 100km Two cyclists start simultaneously from A to B.The speed of first cyclist is 10km/hr greater than that of the other. The first cyclist stops on his way to B and rests for50 minutes but still he is the first to arrive at B. The speed of the first cyclist is \n" ); document.write( "

Algebra.Com's Answer #680071 by KMST(5328) $\"\"$ $\"About$

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At a speed of $\"x\"$ kph (kilometers per hour),
\n" ); document.write( "the second cyclist cover $\"100\"$ km in
\n" ); document.write( " $\"100%2Fx\"$ hours.
\n" ); document.write( "The second cyclist, at $\"x%2B10\"$ kph,
\n" ); document.write( "would cover the same distance in
\n" ); document.write( " $\"100%2F%28x%2B10%29\"$ hours,
\n" ); document.write( "but takes a break lasting $\"50%2F6=5%2F6\"$ hours,
\n" ); document.write( "so his/her trip takes $\"100%2F%28x%2B10%29%2B5%2F6\"$ hours.
\n" ); document.write( "The problem says the first cyclist trip took less time,
\n" ); document.write( "so $\"100%2F%28x%2B10%29%2B5%2F6%3C100%2Fx\"$ is our inequality.
\n" ); document.write( "Multiplying both sides of the inequality times
\n" ); document.write( "the positive number $\"6x%28x%2B10%29\"$ , we get
\n" ); document.write( " $\"600x%2B5x%28x%2B10%29%3C600%28x%2B10%29\"$
\n" ); document.write( " $\"600x%2B5x%5E2%2B50x%3C600x%2B6000%7D%7D%0D%0A%7B%7B%7B5x%5E2%2B50x%3C6000\"$
\n" ); document.write( " $\"5x%5E2%2B50x-6000%3C0\"$
\n" ); document.write( "Dividing by 5 both sides of the inequality, we get
\n" ); document.write( " $\"x%5E2%2B10x-1200%3C0\"$
\n" ); document.write( "You know that the quadratic polynomial
\n" ); document.write( " $\"x%5E2%2B10x-1200\"$ is negative only between its zeros.
\n" ); document.write( "The solutions to
\n" ); document.write( " $\"x%5E2%2B10x-1200=0\"$ <---> $\"%28x-30%29%28x%2B40%29=0\"$
\n" ); document.write( "are $\"x=30\"$ , and $\"x=-40\"$ ,
\n" ); document.write( "and since speeds should not be negative,
\n" ); document.write( " $\"0%3C=x%3C30\"$ ---> $\"10%3C=x%2B10%3C40\"$ is the solution.
\n" ); document.write( "The second cyclist may be moving at 0 kph (sitting still),
\n" ); document.write( "and then the first one would be going at 10kph,
\n" ); document.write( "or they both may be moving,
\n" ); document.write( "but the first cyclist is moving at
\n" ); document.write( "10 kph or more, but less than 40 kph.\r
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