Step-by-step explanation:
12 in long requires 96 pounds.
inversely proportional means that if I double the length of the handle, I need only half of the force.
so,
24 in long requires 48 pounds.
the product of both factors is constant for the system.
c = 12×96 = 1152 = 24×48 = ...
c is called "work". it is force times distance and usually expressed in joules.
(a)
so, the force is then work / distance.
force = 1152 / length
(b)
60 = 1152 / length
60 × length = 1152
length = 1152/60 = 288/15 = 96/5 = 19.2 in
the handle must be 19.2 in long to do the same work with 60 pounds of force (i.e. to loosen the bolt with 60 pounds of force).
