A person walks up a stationary escalator in t1 second. If he remains stationary on the escalator,then it can take him up in t2 second. If the length of escalator is L,then how much time would it take him to walk up the moving escalator?
Answers
Case1:
V1= L/1. {speed=distance/time}
Case2:
V2=L/2
Case3:
V3=V1+V2
=3L/2
Now
Distance =speed*time
L=3L/2 *T
T=2/3 seconds
Answer:
10 seconds.
Explanation:
We call going from the bottom of the escalator to the top a "flight". Let $E$ be the escalator's speed in flights per minute, and let $B$ be Boris's unassisted running speed in flights per minute (a flight is one trip from the bottom to the top). Boris can run up the up escalator in $1/10$ of a minute, so he could run $10$ up-escalator flights in a minute. When he's running up the up escalator, the escalator works with him, so he gains both $E$ flights a minute (from the escalator) and $B$ additional flights (from his own running). Therefore, we must have $B+E=10$.
When Boris runs up the down escalator, the escalator works against him, so he loses $E$ flights each minute, while he still gains $B$ flights a minute from his own running. Since he can make it up the down escalator in $30$ seconds, he can run $2$ flights a minute up the down escalator. So, we must have $B-E = 2$.
Adding our values for $B+E$ and $B-E$, we have
\begin{align*}
(B+E)+(B-E) &= 10 + 2,\text{ so} \\
2B &= 12
\end{align*}and so $B=6$. This means that Boris's unassisted speed is $6$ flights per minute. Thus, it takes Boris $1/6$ of a minute, or $\boxed{10\text{ seconds}}$, to run up the stairs.