The maximum safe load that a rectangular beam can support varies directly with the width w and the square of the height h and inversely with the length L of the beam. A 6-foot-long beam that is 2 inches high and 4 inches wide has a maximum safe load of 1000 pounds.

(a) What is the maximum safe load for a 10-foot-long beam that is 4 inches high and 4 inches wide?

(b) How long should a 4 inch beam be to safely support a 6000-pound load?