Question

The force F (in pounds) needed on a wrench handle to loosen a certain bolt varies inversely with the length L (in inches) of the handle. A force of 40 pounds is needed when the handle is 7 inches long. If a person needs 20 pounds of force to loosen the bolt, estimate the length of the wrench handle. Round answer to two decimal places if necessary.

in inches

Answer 1

14 inches

Explanation:

Since F is inversely proportional to L,

`f = (k)/(l) \\ when \: f = 40 \: l \: = 7 \\ (k)/(7) = 40 \\ k = 280 \\ when \: f = 20 \\ 20 = (280)/(l) \\ l = 14`