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# Boris is playing on the mall escalators.

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Boris is playing on the mall escalators. One escalator goes up, one goes down, and one is out of service; otherwise, they're all identical. The up and down escalators go at the same speed. You can assume that Boris always runs at the same speed. Boris can run up the up escalator in 6 seconds. He can run up the down escalator in 30 seconds. How long does it take him to run up the out-of-service escalator? Explain your answer.

Guest May 6, 2017
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Let the rate that Boris can run  = R

Let the rate that the escalator moves = r

When he runs up the up escalator his rate  = (R + r)

When he runs up the down  escalator his rate is (R - r)

And the Distance that he  covers (the escalator's length)  =  L

So..... using Rate * Time  = Distance

L    =  L

(R + r) * 6  =  (R - r) *30

6R + 6r  = 30R - 30r

36r  = 24R

R = (36/24)r

R =  (3/2)r    →   r  = (2/3)R

So.......using  Distance / Combined Rates   = Time

And substituting for r, we have that

L / (R + r)   =   6    →    L / [ R + (2/3)R]  =  6  →  L / [ (5/3)R]  = 6   →

(3/5)L / R  = 6 →

L/ R   = (5/3) (6)  =    10 seconds to run up (or down) the out of service escalator

CPhill  May 6, 2017
edited by CPhill  May 6, 2017