Roger gets on the elevator at the 41st floor of a skyscraper and rides up at the rate of 42 floors per minute. At the same time, Edward gets on an elevator at the 81st floor of the same skyscraper and rides down at the rate of 78 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross?

• Edward at 81st floor rides down at 78 floors/min.
  Roger at 41st floor rides up at 42 floors/min.
  As, they are travelling in opposite direction, their relative speed = (78+42) floors/min = 120 floors/min.
  So, time taken when they cross = Difference of floors / Speed = (81-41) / 120 min = 1/3 min.
  In 1/3 min, floor at which Roger will be = 41 + 42*1/3 = 55th OR Edward will be = 81 - 78*1/3 = 55
  Therefore, they will cross at 55th floor.
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