Math Is Fun Forum

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Linear Equations - The Escalator

If you walk 26 steps down an escalator you need 30 seconds to reach the bottom. If you take 34 steps, you only need 18 seconds to reach the bottom.

Show that if the escalator is stationary, you have to walk 46 steps to get to the bottom.

Aaargh! I can't draw a graph for this or find an equation, it's like nothing i've learnt so far!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Linear Equations - The Escalator

You need to get 2 simultaneous equations out of this that will help you find the escalator's length and speed.

The first time, you walked 26 steps down the escalator and the escalator took you down the rest of it in 30 seconds. So L = 26 + 30v. (L is length, v is speed)

Similarly, the second equation is L = 34 + 18v.

As both equations are equal to L, you can equate them with each other.

26 + 30v = 34 + 18v.
12v = 8
v = 8/12 = 2/3.

Therefore, the escalator takes you down 2/3 of a step every second.

Substituting that into the first equation gives you that L = 34 + 18*(2/3) = 34+12 = 46, so the escalator has 46 steps.

And naturally, if the escalator isn't moving then you'd need to go down all 46 of them yourself.

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Why did the vector cross the road?
It wanted to be normal.