Escalator Step Math Problem

The problem is a twist on one of my favorite math contest problems from back when i was in high school problem 10 from the 1987 aime.

Escalator step math problem.

I run up the escalator at a constant speed in the direction of the stairs and write down the number of steps a we climbed. Here is our solution. Just as they step on the escalator paint the first step red so that you can see how it progresses relative to how they progress. If the escalator shows 10 steps and goes down in this problem it shows 15 steps and goes down solving for n would give 10 and only the velocity would be negative.

And i ll end with a bit of nit picking. Problem 6 rohan walked down a descending escalator and took 40 steps to reach the bottom. Here s our discussion of the version of the of the problem in chapter 7 of the aops s introduction to algebra. Sohan started simultaneously from the bottom taking 2 steps to every 1 step taken by rohan.

The man has walked up 28 steps so the red step is 28 steps behind him. This is a great problem. Escalator problems in time distance and speed examples. Today he had some difficulty with a problem about an escalator.

In this section we will learn how to solve escalator problems in the topic time distance and speed. Time taken by rohan to reach the bottom from the top is the same as time taken by sohan to reach the top from the bottom. We then drew a diagram of the situation just as the man reaches the top. If a 24 and b 264 how many steps are visible at any one time on the escalator.

Frank and ronnie embarked on a moving escalator to the second floor of a shopping mall.