Let's do an experiment to see the rate an escalator moves at; using the pythagorean theorum. We will express the rate in feet per second and miles per hour.

The length from the start to the end of the escalator is 363 inches = A.

The distance from the top of the escalator to the bottom is 208 inches = B.

The length from the first step of the escalator to the last step is 418.37 inches = C.

The Pythagorean Theorem states that a^2 + b^2 = c^2

To see if this applies, let's try using this formula in our problem.

363^2 + 208^2 =418.37^2

131769 + 43264 = 175033

The time it takes to go from the beginning to the end of the escalator is 22.5415 seconds.

As you know, distance equals rate X time. d = r t, so let's try this formula and see if it works.

208 = r (22.5415) gives r = 208/22.5415 = 9.23 inches per second for the vertical rate.

Therefore, the vertical rate is .524 mph after a conversion of units.

Likewise:

363 = r (22.5415) gives r = 363/22.5415 = 16.10 inches per second for the horizontal rate.

Therefore, the horizontal rate is .915 mph after unit changes.

Using .524 mph and .915 mph rates in the Pythagorean Theorem,

we find that the mph rate is 1.055 mph going up the escalator.

1.055 mph is equal to 18.56 inches per second.

For more information and ideas about this project you may link to a page written by one of the following math artists: Danielle, Darlene, Kellie, Jill, Nanyal, Kevin, Crystal, Rachel, Christina, Jennifer's Second and Fourth Web Page, Candice, Vincent, Esther and Melinda. Most of us are in this picture but not in order of names.