15.( 1) As can be seen from the picture, the average speed of the library is 900 meters away from home (2)? 20=45 m/min, the speed when coming back is 15m/ min, and the average speed when coming back is 60m/ min, 900? 60= 15 minutes, 20+ 10+ 15=45 minutes, and the time to get home is 8: 45. Given the coordinates of two points (30,900) (45,0), the functional relationship y=-45x+2700 can be obtained.

16.( 1) Scheme1:y = 50x-25x-0.5x× 2-30000 Simplified y=24x-30000.

Scheme 2: Y = 50x-25x0.5x× 14 Simplified y= 18x.

(2) According to the question 1, the profit of scheme 1 is y = 24× 6000-30000y =114000.

The profit of scheme 2 is y =18× 6000y =108000.

So choose the scheme 1.