Moving Up - Futility Closet

Moving Up

My wife and I walk up an ascending escalator. I climb 20 steps and reach the top in 60 seconds. My wife climbs 16 steps and reaches the top in 72 seconds. If the escalator broke tomorrow, how many steps would we have to climb?

	Select Click for Answer
Let x be the number of steps on the escalator. I climb x – 20 steps in 60 seconds, and my wife climbs x – 16 steps in 72 seconds. This means the escalator ascends at a rate of 4 steps every 12 seconds, or 20 steps in 60 seconds. Its length is the sum of these 20 steps and the 20 steps I climb, or 40 steps.

June 28, 2014July 6, 2014 | Puzzles