I need help with this question:

Question

After taking the Metro to Dupont Circle in Washington, DC, Jess reached street level by walking up the escalator at a brisk rate, taking 39 steps during

the trip to the top. Suddenly curious about the length of the escalator,

Jess returned to the bottom and walked up the same escalator at

a leisurely rate, taking steps one fourth as often as on the first trip, taking 12 steps in all. How many steps can

be seen on the visible part of the escalator?

I want to understand how the escalator works, and I think a physical diagram would show me best.

Answer 1

At the time when x steps disappear in a fast walk upwards, the total number of steps will be x+39.

Similarly, at a slower walking rate, 4x steps will disappear, so the total number of steps is 4x+12.

The number of these steps is equal, so we have,

x +39 = 4x +12

27 = 3x

x = 9

x + 39 = 9 +39 = 48