The safe load, L, of a wooden beam of width w, height h, and length L, supported both ends, varies directly as the product of the width and the square of the height, and inversely as the length.

Question

The safe load, L, of a wooden beam of width w, height h, and length L, supported both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 3 inches wide, 6 inches high, and 240 inches long can hold a load of 2060 pounds. What load would a beam 4 inches wide, 7 inches high, and 120 inches long, of the same material, support. ( round off your answer to the nearest integer)

Answer 1

L = k*w*h^2/ l

2060 = k*3*6^2/240

k = 4577 and 7/9

So then

L = (4577 and 7/9)*4 * 7^2 / 120 = 7477