the safe load of a wooden beam

Question

the safe load l of a wooden beam supported at both ends varies jointly as the width, w, and the square of fhe depth, d and inversly as ghe length, l. A wodden beam 4in wide, 7 in deep, and 10 ft long holds up 47179lb. What load would a beam 6in wide, 3in deep, and 19ft long support?

Answer 1

The first sentence can be expressed by the equation

L = cw√d/l (1)

where L is the load, and

c is some unknown constant.

The second sentence can be expressed by plugging the given numbers into (1)

47179 = c4√7/10 (2)

The last sentence calls for calculating

L = c6√3/19

We can calculate L if we know c, which we can get from (2)

L = (47179×10/4√7)6√3/19 = 24383.6