The maximum force F (in pounds) needed to tighten the lug nuts on a car tire varies inversely with the length of the wrench L.

Question

The maximum force F (in pounds) needed to tighten the lug nuts on a car tire varies inversely with the length of the wrench L. For a wrench that is 8 inches, 150 pounds of force is required. How much force should be used for a 10-inch long wrench?

Answer 1

Inverse variation satisfies the relation

F₁L₁ = F₂L₂ ⇒

F₂ = (L₁/L₂)F₁

F₁ = 150 lbs

L₁ = 8 in

L₂ = 10 in

Plug in the numbers and get F₂ in units of pounds.