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?

Answer 1

48

Explanation:

If x steps disappear in the time it takes you to briskly walk to the top, then the total number of steps is x+39.

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

These numbers of steps are equal, so we have ...

x +39 = 4x +12

27 = 3x . . . . . . . . . subtract 3x+12

9 = x . . . . . . . . . . . divide by 3

x + 39 = 9 +39 = 48 . . . . The number of visible steps.