The escalator lowered a person walking along it in t (1) = 1 min. If a person walks twice as fast, he will

| June 21, 2021 | education

The escalator lowered a person walking along it in t (1) = 1 min. If a person walks twice as fast, he will descend in 45 seconds. How long does it take for a person to descend while standing on an escalator?

t1 = 1 min = 60 s.

t2 = 45 s.

t -?

S is the length of the escalator, V is the speed of the escalator, Vh is the speed of a person relative to the escalator.

t1 = S / (V + Vh).

t2 = S / (V + 2 * Vh).

From the first and second equalities, we express the length of the escalator: S = t1 * (V + Vh), S = t2 * (V + 2 * Vh).

t1 * (V + Vh) = t2 * (V + 2 * Vh).

60 * V + 60 * Vh = 45 * V + 45 * 2 * Vh.

15 * V = 30 * Vh.

V = 2 * Vh.

S = 60 * (V + Vh) = 60 * (2 * Vh + Vh) = 180 * Vh.

t = S / V = 180 * Vh / 2 * Vh = 90 s.

Answer: a person will descend while standing on the escalator in time t = 90 s.



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