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 one third

Question

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 one third foot wide, one fourth foot high, and 14 feet long can support 20 tons, find how much a similar beam can support if the beam is two thirds foot wide, one half foot high, and 20 feet long.

Answer 1

First the vocabulary:

"jointly" means attached by multiplication 

"inversely" means it's in the denominator

Implied is "k" the constant, that's always there, even if unmentioned.

So we've got:

M = max weight that beam can support.
And these dimensions of a beam:
W = width
H = height
L = length

So:

M = k(WH²)/L

Let's solve for k by substituting in the values from the first beam! 
20=k[(1/3)(1/4)²]/14

20 = k[(1/3)(1/16)]/14

 

20 = k(1/48)/14

20=k(1/48)(1/14)
20(48)(14) = k
13440=k

 

Now we substitute the value of k into our original equation:
M= (13440)WH²/L

now pop in the values of the 2nd beam:
M = 13440[(2/3)(1/2)²]/20

and compute!