David gets on the elevator at the 11^th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

Suppose their paths cross after x minutes
Then,
11 + 57x = 51 - 63x
⇒ 57x + 63x = 51 - 11
⇒ 120x = 40
⇒ x = $$\frac{1}{3}$$
Number of floors covered by David in $$\frac{1}{3}$$ min.
$$\eqalign{ & = {\frac{1}{3} \times 57} \cr & = 19 \cr} $$
So, their paths cross at (11 + 19) i.e., 30^th floor