It takes avi one half-hour longer to make a basket than it takes markus. after 28 hours, markus has made one more basket than avi has made. how many hours does it take avi to make one basket?

If Avi takes x hours to make 1 basket then it takes Markus   x - 0.5 hours.
Avi makes 1/x baskets in 1 hour and Markus makes 1/(x - 0.5) baskets in 1 hour. 

so we have the equation:-

28 /( x - 0.5) - 28/x = 1

28x - 28(x - 0.5) = x(x - 0.5)

x^2 - 0.5x -14 = 0
x = 4 , -3.5  (ignore the negative) 

x = 4

It takes Avi 4 hours to make one basket.