When you push down on the handle of a bicycle pump, a piston

Question

in the pump cylinder compresses the air inside the cylinder.
When the pressure in the cylinder is greater than the pressure
inside the inner tube to which the pump is attached, air begins to
flow from the pump to the inner tube. As a biker slowly begins
to push down the handle of a bicycle pump, the pressure inside
the cylinder is 1.0 x 10^5 Pa, and the piston in the pump is 0.55 m
above the bottom of the cylinder. The pressure inside the inner
tube is 2.4 x 10^5 Pa. Calculate how far down must the biker push
the handle before air begins to flow from the pump to the inner
tube. Ignore the air in the hose connecting the pump to the inner
tube, and assume that the temperature of the air in the pump
cylinder does not change.