MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C785BA.61A84F20" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C785BA.61A84F20 Content-Location: file:///C:/753AC877/2007prob7.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Problem 7

Pro= blem 7

 

Joe= and Sam are walking up an escalator.  = Joe walks twice as fast as Sam. Joe takes 27 steps to arrive at the top, and Sam takes 18 steps to arrive at the top.  How many of the upward moving escalator steps are visible at any tim= e?

 

[Problem submitted b= y Juergen Pahl, LACC Profes= sor of Mathematics.]

 

 

 

Solution A for Pr= oblem 7:

 

Whe= n Joe arrives at the top, Sam has only taken 13.5 steps.  That means he is only  of his way = up. By the time Joe gets to the top, the escalator has carried him up an additional number of x steps.  When Sam is ¾ of his way up, he has also been carried up an additional number of= x steps.

 

If = V is the number of visible steps, then

        =             &nb= sp;              for Joe, and

        =             &nb= sp;              for Sam.

Sol= ving for x:   

        =             &nb= sp;            

 

The= refore the number of visible steps is .

 

Solution B for Pr= oblem 7:

 

Let= u be the speed of the elevator, v and 2v be the speed= of Sam and Joe respectively when the elevator is not moving.=

 

 

Apparent speed

time

Distance in steps

Sam

u+v

=

= =

Joe

u+2v

=

=

The distances traveled are the same.

 =3D   distance = =3D 54.

 

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