You take an elevator from the ground floor to the top of the empire state building, a building 102 stories high. (a) what is the work done on you by gravity? (assume that your mass is 78 kg and that the height of the empire state building is 300 m.) -229320 correct: your answer is correct. j

The work done is the change in gravitational potential energy from the bottom to the top.

M g H = (78 kg) (9.81 m/s²) (300 m) = 229,320 joules .

That's the AMOUNT of work done.  Now the question is:  Who or what does the work ?

You have to be lifted against the force of gravity, by something ...
some strong men, an army of hamsters, an electrical elevator, etc.
They have to exert an upward force equal to your weight, and
keep it going until you're 300 meters off of the ground.
Whatever it is that lifts you is what does the work.

Gravity certainly exerts a force on you all the way, but the distance
you move is in the direction OPPOSITE to gravity.  If you want to
calculate the amount of work done by gravity, using the formula

Work = (force) x (distance) ,

then since the force and the distance are in opposite directions,
their signs must be opposite, and you'd have to write

 Work = (m g h) = (78 kg) (9.81 m/s²) (-300m) = -229,320 joules.

The elevator has taken 229,320 joules of energy AWAY from gravity,
and stored it in you.  That's now YOUR gravitational potential energy,
as long as you stay at the top.  If you let go, or jump, or sail away in
a parachute, or come DOWN the stairs, gravity will DO that much 
work on you to bring you down to Earth again. 

If football was tossed in air without gravity or friction the ball would go into space