# Riddler Express for 22 June 2018

Spoiler for last week’s fivethirtyeight.com Riddler Express:

From Dave Moran, this is the final boarding call for flight RDLR 100:

Michelle decided to get some extra exercise at the airport by walking toward her departure gate at her normal pace, but on a lengthy moving walkway … going the wrong way. Gotta get those steps in.

After going 100 meters (that is, getting 100 meters closer to her departure gate), Michelle dropped her boarding pass onto the walkway. But she didn’t notice at first and continued walking toward her gate. After walking another 90 seconds, she finally realized that she had dropped her boarding pass. She then immediately turned around and jogged in the direction of the walkway’s movement. Michelle’s jogging pace is exactly twice as fast as her walking pace. She caught up with her boarding pass 10 meters from the start of the moving walkway.

How fast does the walkway move?

You could set this up as a complicated algebra problem, or you can be lazy enough to be clever.

Think about this from the boarding pass’s point of view. As far as it’s concerned it’s sitting still while Michelle walks at her normal walking speed away from it for 90 seconds, and then jogs back to it at twice that speed. She’s covering the same distance both times, so it takes her 45 seconds to return to where she dropped the pass after she turns around; that is, the pass is lying on the walkway for 135 seconds.

Now, from the airport’s point of view, the pass is moving at the speed of the walkway and it covers 90 meters in those 135 seconds. So that speed is 90 / 135 = 2/3 meters per second.