It’s not just the pressure you’re fighting against; you also have to consider the volume. It takes many more strokes of the pump to add a “pound of air” to the car tire than to the bike tire.
What people loosely call a “pound of air” is not an amount of air, like a pound of butter; it’s a pressure: pounds of force per square inch, generally abbreviated psi. That force is the cumulative effect of the zillions of air molecules in the tire, which are continually bombarding every square inch of the inner walls.
The more air molecules you force into a tire, the more bombardment there will be and the higher the pressure will be. That’s why adding more air increases the pressure.
As you’ve surmised, it should be harder to force air into a 60-psi tire than into a 30-psi tire. That’s because the air molecules inside a tire are also bombarding the valve opening, making it harder to force more molecules through.
So each stroke of your pump does indeed require more effort to overcome the bike’s 60 psi of pressure than to overcome the car’s 30 psi. You have to use twice as much force on the pump handle to push air into the bike tire.
Then why is it more work to pump up the car tire?
A typical car tire contains about six or eight times as much air space as a typical bike tire. In order to have the same pressure, the same rate of molecule bombardment per square inch, in both tires, there would have to be six or eight times as many air molecules present in the car tire.
Therefore, to increase the car tire’s pressure by each psi, you have to pump in six or eight times as much air, using six or eight times as many strokes, as you do to get a psi of pressure into the bike tire. Even though each stroke takes half the effort, you’re still working more than three times as hard.
