An airplane is preparing to land at an airport. it is 51,300 feet above the ground and is descending at the rate of 3,000 feet per minute. at the same airport, another airplane is taking off and will ascend at the rate of 2,700 feet per minute. when will the two airplanes be at the same altitude and what will that altitude be ?

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.