A person walking down the escalator descends in 80 seconds. If a person walks twice as fast, he will descend in 60 s

| February 10, 2021 | education

A person walking down the escalator descends in 80 seconds. If a person walks twice as fast, he will descend in 60 seconds. How long will the descent take from a person standing on an escalator

S = V * t, S – distance, V – speed, t – time.
Descent distance:
S = (Ve + V1) * t1, where Ve – escalator speed, V1 – human speed, t1 = 80 s.
S = (Ve + V2) * t2, where V2 is the increased speed of a person (V2 = 2 V1), t2 = 60 s.
S = Ve * t3.
(Ve + V1) * t1 = (Ve + V2) * t2.
(Ve + V1) * t1 = (Ve + 2V1) * t2.
Ve * t1 + V1 * t1 = Ve * t2 + 2V1 * t2.
Ve * 80 + V1 * 80 = Ve * 60 + 2V1 * 60.
Ve * 20 = 40V1.
Ve = 2V1.
(Ve + V1) * t1 = Ve * t3.
(2V1 + V1) * t1 = 2V1 * t3.
3V1 * t1 = 2V1 * t3.
t3 = 3t1 / 2 = 3 * 80/2 = 240/2 = 120 s.
Answer: Descent will take 120 seconds.



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