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

Entered answer:

✅ Correct Answer: 60

When you walk on an escalator, your speed and the escalator's speed add together!

Let's use simple variables:

$v =$ Moody's normal walking speed

$e =$ escalator's speed

$L =$ length of escalator

Scenario 1: Normal speed, takes 30 seconds

Combined speed $= v + e$

Distance $=$ Speed $\times$ Time,

so: $L = (v + e) \times 30$

Scenario 2: Double speed, takes 20 seconds

Combined speed $= 2v + e$

Distance $=$ Speed $\times$ Time, so: $L = (2v + e) \times 20$

Since both expressions equal $L$ :

$(v + e) \times 30 = (2v + e) \times 20$

$30v + 30e = 40v + 20e$

$30e - 20e = 40v - 30v$

$10e = 10v$

$e = v$

From scenario 1:

$\begin{aligned} L &= (v + e) \times 30 \\ &= (v + v) \times 30 \\ &= 2v \times 30 \\ &= 60v \end{aligned}$

When Moody stands still, only the escalator moves at speed $e = v$ :

Time $= \dfrac{L}{e} = \dfrac{60v}{v} = 60$ seconds

Answer: 60 seconds

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