Inverse word problem

Question

The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 4 inches wide, 9 inches high, and 240240 inches long can hold a load of 6810 pounds. What load would a beam 3 inches wide, 8 inches high, and 144 inches long, of the same material, support? (Round off your answer to the nearest integer.)

Answer 1

I assume that you mean 240 inches, not 240240inches (that's 3.79 miles!!).

 

L = kwh²/l  Since L = 6810 when w=4, h=9, and l=240, 6810 = k(4)(9)²/(240)

 

                                                                                  k = 5044.4444

 

So, L = 5044.4444wh²/l. 

 

Therefore, when w=3, h=8, and l=144, L = 5044.4444(3)(8)²/(144) ≈ 6725.9 pounds