document.write( "Question 1149393: Mary and John have both completed a trip up an escalator. John took 15 steps on the way up and took 12 seconds to reach the top. Mary took only 7 steps, and took 18 seconds to reach the top. How many steps does the escalator have in total? \n" ); document.write( "

Algebra.Com's Answer #770734 by greenestamps(13203) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Let x be the number of steps on the escalator.

\n" ); document.write( "Since John took 15 steps while on the escalator, the number of steps the escalator moved during his time on it was x-15; since Mary took 7 steps while on the escalator, the number of steps the escalator moved during her time on it was x-7.

\n" ); document.write( "Since the escalator moves at a constant rate, the ratio of the numbers of steps the escalator moved during their trips is the same as the ratio of times spent on the escalator. So

\n" ); document.write( " $\"%28x-15%29%2F%28x-7%29+=+12%2F18+=+2%2F3\"$
\n" ); document.write( " $\"3x-45+=+2x-14\"$
\n" ); document.write( " $\"x+=+31\"$

\n" ); document.write( "There are 31 steps on the escalator.

\n" ); document.write( " \n" ); document.write( "

\n" );