1. ## Word Problem #2

On one of the escalators on the London subway I find that if I walk down twenty-six steps I require thirty seconds to get to the bottom, but if I make thirty-four steps I require only eighteen seconds to reach the bottom. What is the height of the stairway in steps? The time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom onto the level platform.

2. Originally Posted by bearej50
On one of the escalators on the London subway I find that if I walk down twenty-six steps I require thirty seconds to get to the bottom, but if I make thirty-four steps I require only eighteen seconds to reach the bottom. What is the height of the stairway in steps? The time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom onto the level platform.

Think about it this way: how far do you actually move down? In either case you are going the same distance, so the two cases will equal each other (and they will be calculated the same way). You just need to figure out how they are calculated.

There are two components to the distance you are travelling. The first component is the movement of the escelator itself. This is a simple "distance equals rate times time" expression, where the rate is unknown (you do know how long it takes). The second component is the movement of you stepping down the escelator. Add these two components together and you have the distance you've travelled.

Since there is a variable involved, you need to set the first case equal to the second and solve for the rate at which the escelator is travelling. You can then use that rate to figure out how far you've actually travelled.

Hope this helps. Think about it and give it a try. Let me know if you need more help. Hint: the escelator is 46 steps tall.

3. Hi,
It's very simple: 26 steps you walk down, you have 30 seconds left
-----------------34 steps you walk down, you have 18 seconds left
Now consider this: 34 - 26 = 8 . So every 8 steps you walk down while the escalator rolling down, it takes 12 seconds.
So in 30 seconds you walk down while the stairs moving down you will walk (30x8)/12 = 20 steps; in addtion to 26 steps that you have walked, it totals 46 steps.

You can also use the second time you walk to calculate
in 18 seconds you can walk (18x8)/12= 12 steps while the stairs rolling down, plus the 34 steps you have walked you also get 46 steps total.