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# Algebra

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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 36 seconds. How many seconds does it take him to run up the out-of-service escalator?

Apr 15, 2022

#1
+126978
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This is similar to the type of problem where an airplane flies with  the wind and  then against the wind

Running down the up escalator is the same as  running up the down escalator

Let  Boris's  speed  be =  R

Let the speed of the escalator =  S

And R > S

Call the length of the escalator  = L

Boris's effective rate with the elevator = (R + S)

Boris's effective rate against the elevator = (R -S)

And  Distance    =   Rate * Time

L   =  L

6 ( R + S)  = 36 ( R - S)

6R + 6S  = 36R - 36S

42S = 30R

7S = 5R

R = (7/5)S

And     Length of escalator / ( R + S)  =   6

So

L / ( R + S)  = 6

L / [ (7/5)S + S ]  = 6

D / [ (12/5 ) S ]  =  6

D / S    =  6 ( 12/5)  =    (72  / 5 )  =   length of time for Boris to navigate the out-of service escalator  =  14.4 sec

Apr 15, 2022
edited by CPhill  Apr 15, 2022