How to Solve Escalator Speed Problems
Solve escalator aptitude problems using relative speed — effective speed with and against motion — with worked examples and practice questions.
Expected Interview Answer
Escalator problems are relative-speed problems where the escalator itself contributes a constant speed e (in steps or distance per unit time) that adds to a person walking up and subtracts from a person walking down, so the total visible steps N stays fixed while effective speed changes with direction.
If a person walks up at speed p while the escalator moves up at speed e, their effective speed relative to the ground is p+e, and the number of steps they personally take is p × (N/(p+e)) — fewer steps than N because the escalator carries them part of the way. Walking down against an upward-moving escalator gives effective speed p−e (must have p>e to make progress), while walking down with a downward-moving escalator gives p+e. Two scenarios (e.g., walking up at speed p1 takes t1 steps, walking up at speed p2 takes t2 steps) give two equations in N and e that can be solved simultaneously. The escalator’s own step count N is constant regardless of the walker’s speed — only the number of steps the person personally climbs changes.
- Treats the escalator as a constant relative-speed contributor, just like a moving walkway or river current
- Two-scenario setups (different walking speeds) solve for both N and e simultaneously
- Distinguishes total visible steps N from steps actually taken by the walker
AI Mentor Explanation
A ground announcer’s scrolling scoreboard message moves at its own constant speed across the display, and a spectator’s eye scanning in the same direction “walks” the message faster (reading speed plus scroll speed) while scanning against it is slower (reading speed minus scroll speed) — the total message length stays fixed, only how fast you personally cover it changes. Escalator problems work identically: the escalator’s constant speed adds when you walk with it and subtracts when you walk against it, while the visible step count N never changes.
Worked example
Scenario 1
- p=2 steps/s, 20 own steps
- N = (p+e) × 10
Scenario 2
- p=4 steps/s, 12 own steps
- N = (p+e) × 3
Solve
- Two equations, two unknowns (N, e)
Step-by-Step Explanation
Step 1
Identify direction and effective speed
Same direction as escalator: p+e. Opposite direction: p−e.
Step 2
Relate personal steps to time
Time on escalator = personal steps taken ÷ personal walking speed p.
Step 3
Express total visible steps N
N = effective speed × time spent on the escalator.
Step 4
Solve simultaneous equations
Use two different walking-speed scenarios to solve for N and e together.
What Interviewer Expects
- Correct effective-speed setup (p+e or p−e) based on direction
- Distinguishing total steps N from steps personally taken by the walker
- Setting up and solving two equations for two unknowns (N and e)
- Sanity-checking that p > e is required when walking against the escalator’s direction
Common Mistakes
- Confusing total visible steps N with the number of steps the person actually takes
- Adding speeds when walking against the escalator (should subtract)
- Forgetting the escalator continues moving even while the person is not stepping
- Setting up only one equation when two unknowns (N and e) require two scenarios
Best Answer (HR Friendly)
“I treat the escalator like a constant current: if I walk in the same direction it is moving, my effective speed is my walking speed plus the escalator’s speed, and if I walk against it, it is my speed minus the escalator’s speed. The total number of visible steps on the escalator never changes — what changes is how many steps I personally have to take, since the escalator carries me part of the way. When I am given two different walking speeds and how many steps each takes, I set up two equations and solve for both the total steps and the escalator’s own speed together.”
Follow-up Questions
- How would the problem change if the escalator itself stopped moving?
- How do you find the time saved by walking versus standing still on the escalator?
- How does this generalize to boats moving with and against a river current?
- How would two people walking at different speeds in opposite directions on the same escalator interact?
MCQ Practice
1. A person walks up a moving escalator taking 20 of their own steps, covering the whole visible length in 10 seconds. If the escalator were stopped, they would need to take how many steps (walking at the same personal step rate) if there are 30 total visible steps?
With the escalator stopped, the person must personally cover all 30 visible steps.
2. Walking speed p and escalator speed e are in the same direction. The effective speed relative to the ground is?
Same-direction motion adds the escalator’s speed to the walker’s own speed.
3. A person walks down against an upward-moving escalator. For them to make forward progress, which condition must hold?
The walker’s own speed must exceed the escalator’s upward speed, or they never reach the bottom.
Flash Cards
Effective speed walking with the escalator? — p + e (personal speed plus escalator speed).
Effective speed walking against the escalator? — p − e (requires p > e to make progress).
What stays constant regardless of walking speed? — The total visible number of steps, N.
What changes with walking speed? — The number of steps the person personally takes and the time spent on the escalator.