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Malik walked up and back down an empty 18 m18\,\text{m} long escalator at a constant rate. Since the escalator was going up at the time, it took him only 22.5 s22.5\,\text{s}. Going down took Malik 90 s90\,\text{s}. Assume the escalator speed is constant.\newlineWhat was Malik's walking speed?

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Full solution

Q. Malik walked up and back down an empty 18 m18\,\text{m} long escalator at a constant rate. Since the escalator was going up at the time, it took him only 22.5 s22.5\,\text{s}. Going down took Malik 90 s90\,\text{s}. Assume the escalator speed is constant.\newlineWhat was Malik's walking speed?
  1. Calculate Escalator Speed: Calculate the speed of the escalator.\newlineSpeed = DistanceTime\frac{\text{Distance}}{\text{Time}}\newlineEscalator speed = 18 m22.5 s\frac{18\,\text{m}}{22.5\,\text{s}}\newlineEscalator speed = 0.8 m/s0.8\,\text{m/s}
  2. Calculate Malik's Speed: Calculate Malik's speed going up.\newlineTotal speed going up = Escalator speed + Malik's walking speed\newlineLet Malik's walking speed be xx m/s.\newline0.80.8 m/s ++ xx m/s == 18m/22.5s18m / 22.5s\newlinex=(18m/22.5s)−0.8x = (18m / 22.5s) - 0.8 m/s\newlinex=0.8x = 0.8 m/s −- 0.80.8 m/s\newline0.80.800 m/s

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