Walking Up An Ascending Escalator

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?

Here is way to find the total number of steps! 

Total Steps on Broken Escalator

What was the question?

Climbing 16 steps makes you to reach at the top in 72 seconds but if you climb 20 steps then it requires 60 seconds only.

That means, climbing 4 steps extra pushes you at the top saving 12 seconds. This is the speed of the escalator which is 4 steps per 12 seconds.

That is escalator speed is 1 step per 3 seconds and 20 steps per 60 seconds. But in 60 seconds I climb 20 steps more hence total steps on escalator must be 40.

This is how escalator pushes me 20 steps + I climb 20 steps = 40 steps in 60 seconds.

On the other hand my wife climb 16 steps + escalator pushes her (40-16) i.e. 24 steps = 40 steps in 72 seconds.  


MATHEMATICAL APPROACH :

Let's suppose there are 'x' steps on escalator. If M is my speed , W is my wife's speed and E is speed of the escalator in terms of steps per second then,

M = 20/60 = 1/3 and W = 16/72 = 2/9.

In my case, for relative speed (steps per second) x/60, we have,

M - E = x/60

1/3 - E = x/60    ...........(1)

And in my wife's case, for relative speed (steps per second) x/72, we have, 
 
W - E = x/72

2/9 - E = x/72  ..............(2)

Subtracting (2) from (1),

(1/3) - (2/9) = (x/60) - (x/72)

(1/9) = x / 360

X = 40

So there are 40 steps on the escalator.