document.write( "Question 498778: A child is running on a moving sidewalk in an airport. When she runs against the sidewalk's motion, she travels in seconds. When she runs with the sidewalk's motion, she travels in the same amount of time. What is the rate of the child on a still sidewalk and what is the rate of the moving sidewalk? \n" ); document.write( "

Algebra.Com's Answer #337172 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"c\"$ = rate of child on stationary sidewalk
\n" ); document.write( "Let $\"s\"$ = rate of moving sidewalk
\n" ); document.write( "Let $\"d\"$ = length of the sidewalk
\n" ); document.write( "Let $\"t\"$ = time spent on moving sidewalk
\n" ); document.write( "given:
\n" ); document.write( "Running against motion of sidewalk
\n" ); document.write( " $\"+d+=+%28+c+-+s+%29%2At+\"$
\n" ); document.write( "Running with motion of sidewalk
\n" ); document.write( " $\"+d+=+%28+c+%2B+s+%29%2At+\"$
\n" ); document.write( "The distance and the time are the same in both cases
\n" ); document.write( " $\"+c+-+s+=+c+%2B+s+\"$
\n" ); document.write( " $\"+-s+=+s+\"$
\n" ); document.write( " $\"+2s+=+0+\"$
\n" ); document.write( "The sidewalk is not moving \n" ); document.write( "

\n" );