The Maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam 1/3 foot wide, 1/4 foot high, and 17 feet long can support 10 tons, Find how much a similar beam can support if the beam is 3/4 foot wide, 1/3 foot high, and 13 feet long.

Maximum weight =k W*H^2/L, where k is a constant.

10 = k(1/3)(1/4)^2/17 = k/816......(1)

x = k(3/4)(1/3)^2/13 = k/156 ......(2)

(2)/(1): x/10 = 816/156 = 68/13

x = 680/13 = 52.31 tons <==Answer