document.write( "Question 1163723: An escalator is moving up. If Zach walks down from the top to the bottom, he walks 120 steps. If he walks up from the bottom, he walks 90 steps. He walks down 2 times as fast as he walks up. Find the number of steps of the escalator when it is not moving. \n" ); document.write( "

Algebra.Com's Answer #787951 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Let n be the number of steps of the escalator when it is not moving  (the \r\n" );
document.write( "unknown value under the problem's question).\r\n" );
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document.write( "Let T be the time for Zack walking down from the top to the bottom of the escalator.\r\n" );
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document.write( "Then the time for Zack walking up from the bottom of the escalator is 2T, according to the condition.\r\n" );
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document.write( "For Zack going down, the speed of the escalator is    steps per unit of time.\r\n" );
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document.write( "For Zack going up,   the speed of the escalator is    steps per unit of time.\r\n" );
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document.write( "The speed is the same, which gives you an equation\r\n" );
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document.write( "     = .\r\n" );
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document.write( "To solve it, cancel factor T in both denominators, then cross multiply and simplify.  You will get\r\n" );
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document.write( "    2*(n-120) = n-90\r\n" );
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document.write( "    2n - 240  = n - 90\r\n" );
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document.write( "    2n - n    = 240 - 90\r\n" );
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document.write( "     n        = 150.\r\n" );
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document.write( "ANSWER.  The number of steps of the escalator when it is not moving is 150.\r\n" );
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