Escalator Speed and Time

CAT 2022 Slot 3 · QA · Medium · Arithmetic

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Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is

Answer

60

Explanation

Let EE be the length of the escalator, mm be Moody's normal speed, and ee be the escalator's speed.

From the given conditions: 30(m+e)=E  ⟹  m+e=E3030(m + e) = E \implies m + e = \frac{E}{30} 20(2m+e)=E  ⟹  2m+e=E2020(2m + e) = E \implies 2m + e = \frac{E}{20}

Subtract the first equation from the second: m=E20−E30=E60m = \frac{E}{20} - \frac{E}{30} = \frac{E}{60}

Substitute mm into m+e=E30m + e = \frac{E}{30}: E60+e=E30  ⟹  e=E60\frac{E}{60} + e = \frac{E}{30} \implies e = \frac{E}{60}

If Moody stands still, his speed relative to the ground is e=E60e = \frac{E}{60}. Time needed to finish riding the escalator =Ee=60 seconds= \frac{E}{e} = 60\text{ seconds}.

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