How can simple machines trade force for distance?
The short answer is that the same work is done in both cases.
It is the principle of conservation of energy.
#"work" = "force"*"distance".
As an example, assume you want to raise a 1000 kg car 0.1 m to do some repair underneath. Let's calculate the work required to lift it 0.1 m without a simple machine.
The weight of the car is
Now, get a fulcrum and a long pole with a cradle that fits under the car. Find the best spot for the fulcrum so that the end of the lever would have to move down 1.96 m to raise the car 0.1 m. Then have a 500 N woman sit on the end. The work done by that woman would be
I hope this helps,