Billy can paint 100 feet of fence in twenty five minutes. Betty can paint 200 feet of fence in 45 minutes. If they both work same amount of time, how much fence can they paint? If they paint \(D\) feet of fence, how much fence each painted and how long did it take to paint this much fence? State the answer using functions, averages, and harmonic averages. Then, find out the points on line \(ax+by=c\) for a,b,c positive which are closest to origin (0,0). Draw the picture to illustrate that answer is possible.