# Math Help - Escalator Question

1. ## Escalator Question

need help with this question.

Walking down a certain escalator descending at a constant rate, if I take 30 seconds to reach the bottom, I have to walk down 13 consecutive steps. If i take 21 seconds to reach the bottom, I have to walk down 19 consecutive steps. The number of steps showing on this escalator at any one time is:
a) 32 b) 33 c) 34 d) 35 e) 36

2. I may be wrong, but I think this is impossible without knowing the speed of the escalator

3. No chokful, although it might not seem like it, there is enough information available.

Originally Posted by foreverbrokenpromises
Walking down a certain escalator descending at a constant rate, if I take 30 seconds to reach the bottom, I have to walk down 13 consecutive steps. If i take 21 seconds to reach the bottom, I have to walk down 19 consecutive steps. The number of steps showing on this escalator at any one time is:
a) 32 b) 33 c) 34 d) 35 e) 36
Walking down 13 steps gave a time of 30 seconds.
Walking down 19 steps gave a time of 21 seconds.

Therefore walking down 6 steps would take a total of $30-21=9$ seconds, giving us a rate of $\frac{6 ~ \text{steps}}{9 ~ \text{seconds}} = \frac{2}{3}$ steps per second.

So the total number of steps on the escalator at any given time is given by

Amount of steps walked down + (Steps per second rate $\times$ Time taken)

I'll leave it to you to work out the answer, make sure you get the same answer for both of the cases (you will )