So the poilet said he was going to take short cuts so we could arrive 15/20 minuets early

:) a little explanation would have helped.

In some countries, flight plans have to be planned and filed with the planned route being along the structured airways, with a lot of twists and turns. Some places even have one-way airways that make you go a few extra blocks. Like below.

But once airborne, and where the air traffic controllers have radar, and no conflicting traffic, they will usually revise the clearances for direct, and cut-across the bends and twists.

A minuet is typically about four minutes. So this means you arrived between 60 and 80 minutes early!

:-)