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Rama gets an elevator at the 11th floor of a multi-storey building and rides up at the rate of 57 floors per minute. At the same time, Somaya gets another elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they travel at these rates, at which floor will they cross each other?





Solution

Let the time after which they meet be t minutes. Rama’s position after t minutes = 11 + 57t Somaya’s position after t minutes = 51 − 63t At the meeting point: 11 + 57t = 51 − 63t ⇒ 120t = 40 ⇒ t = 1/3 minutes. Hence, floor number = 11 + 57 × (1/3) = 11 + 19 = 30.


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