This problem involves inverse variation, which means that the product of the force and the handle length is constant for a given bolt. I can write this as an equation: F * L = K, where F is the force, L is the handle length, and K is the constant. I can use the given information to find the value of K: 375 * 9 = K, so K = 3375. Now I can plug in the new handle length of 15 inches and solve for F: F * 15 = 3375, so F = 3375 / 15, which is 225. Therefore, a wrench of 15 inches will require 225 pounds of force to loosen the same bolt. 
The force needed to loosen a bolt varies inversely with the length of the handle of the wrench used. A wrench with a handle length of 9 inches requires 375 pounds of force to loosen a certain bolt. A wrench of 15 inches will require how many pounds of force to loosen the same bolt?