Numerical answer
Asha walks up a moving 'up' escalator at a constant pace and takes 30 steps to reach the top in 20 seconds. Bina, walking up the same moving escalator at a faster constant pace, takes 40 steps to reach the top in 15 seconds. How many steps of the escalator are visible when it is stationary?
Show answer and solution
Answer: 70
Let the escalator move e steps per second and let N be the number of visible steps.
While a person walks up, the steps they climb plus the steps the escalator carries them add up to N.
Asha: N = 30 + 20e
Bina: N = 40 + 15e
Equating: 30 + 20e = 40 + 15e → 5e = 10 → e = 2 steps/s.
N = 30 + 20 × 2 = 70. (Check: 40 + 15 × 2 = 70 ✓.)
Key idea: Time on the escalator is what links a person's own steps to the escalator's contribution; always write N = (own steps) + (escalator speed × time).
While a person walks up, the steps they climb plus the steps the escalator carries them add up to N.
Asha: N = 30 + 20e
Bina: N = 40 + 15e
Equating: 30 + 20e = 40 + 15e → 5e = 10 → e = 2 steps/s.
N = 30 + 20 × 2 = 70. (Check: 40 + 15 × 2 = 70 ✓.)
Key idea: Time on the escalator is what links a person's own steps to the escalator's contribution; always write N = (own steps) + (escalator speed × time).
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