At the Denver Airport last month, Mr. P noticed the behavior of people on the Moving Sidewalks.   Some people just stood on the walkways; some people walked on the walkways; and some people avoided the walkways.



Seth Young, director of the Center for Aviation Studies at Ohio State University conducted empirical observations at several airports for his doctoral dissertation years ago.   He found that normal walking speed is approximately 3 mph through an airport.   People walking on a moving walkway stride at roughly 2.24 mph, Young found, indicating that they slow down from their normal 3 mph rate.   The moving walkways travel at 123.2 feet per minute.

Using the information above, answer the following questions, leaving your answers to the first three questions in miles per hour (mph):

(1) How fast does a person move who is just standing on a moving sidewalk?
(2) How fast does a person move who is walking on the moving sidewalk?
(3) How fast does a person move who is walking in the airport (not on a moving sidewalk)?
(4) Mr. P observed a youngster who was walking the wrong way on the moving sidewalk (where are the parents?).   It took the youngster 2 minutes to walk the entire length of the walkway the wrong way, but then when he turned around and walked with the walkway, it only took him 24 seconds.   How long was the moving walkway?
Solution to the Problem:

(1) 1.4 mph
(2) 3.64 mph
(3) 3 mph (this was given)
(4) 123.2 feet in length

First, you must convert 123.2 feet per minute to miles per hour using dimensional analysis.


This would be the answer to (1) how fast a person would travel if she were just standing on the walking sidewalk.

For (2), you would just add 1.4 to 2.24 to get 3.64 mph.

The answer to (3) was given in the problem.

In (4), you can set up a rate / time / distance table to solve this algebra problem.
I chose to solve it using minutes and seconds. Let x = rate at which the youngster is walking.
Let y = distance of the walkway.

      Rate     Time     Distance  
  Against walkway       x - 123.2 ft/min       2 minutes       y
  With walkway       x + 123.2 ft/min       .4 min (24 sec)       y

Since RATE x TIME = DISTANCE, you can set up two equations:
(x - 123.2) (2) = y
(x + 123.2) (.4) = y

Substitute for y:
2x - 246.4 = .4x + 49.28
Solving:
1.6x = 295.68
so x = 184.8 ft/min

To determine the length of the walkway, substitute the value for x into one of the two original equations and solve for y:
(x - 123.2) (2) = y
(184.8 - 123.2) (2) = y
So y = 123.2 feet.

Research indicates that the walkways do not save travelers significant time because people tend to walk slower when using the devices.   "Overall, the speed of those on the belt is less than if the belt wasn't there," said Seth Young, director of the Center for Aviation Studies at Ohio State University.

Young conducted empirical observations at several airports for his doctoral dissertation years ago, he said.   He found that normal walking speed is approximately 3 mph through an airport. A typical moving walkway belt travels at 1.4 mph., which is how fast a person would move if they just stood on the belt - or about half the pace of a normal walk speed at an airport.

People walking on a moving walkway stride at roughly 2.24 mph, Young found, indicating that they slow down from their normal 3 mph rate.   The bottom line of the study was that typical users of a moving walkway travel at 3.66 mph, gaining a minor speed increase over the 3 mph speed of not using the walkway at all.

"A good number of folks - about one-third of all pedestrians - just stand there and travel the 1.4 mph speed of the belt," Young said Friday in a phone interview.   "And eventually the 'walkers' get backed up behind the 'standers' and slow down as well."

"So overall, the speed of those on the belt is less than if the belt wasn't there," Young said.

Correctly solved by:

1. Bryce Villanueva Victoria, Minnesota
2. Ivy Joseph Pune, Maharashtra, India
3. Rob Miles Northbrook, Illinois
4. Kimberly Howe Vienna, Virginia


Honorable mention for answering the first three parts correctly:

Faith Pfeifer Mountain View High School,
Mountain View, Wyoming
Linzy Carpenter Mountain View High School,
Mountain View, Wyoming
Hope Pfeifer Mountain View High School,
Mountain View, Wyoming
Frankie Jenkins Mountain View High School,
Mountain View, Wyoming
Gauge Lockhart Delta High School,
Delta, Colorado