It is due to time dilation as predicted by Einstein's relativistic theory.

When you are scheduled to arrive at let's say 1:40pm, it is with reference to the passenger's clock which is traveling with the plane.

However, because the plane is moving so fast, the stationary ground clock runs faster than your clock. Thus, the observed difference, i.e. you "appear" to be 10 mins late.

The solution is, obviously, to take time dilation into account and adjust the arrival time accordingly.

As a side note, it has been experimentally shown by independent observers that booze might also induce time dilation effect