What holds water yet is full of holes?

Matthew leaves home in the morning to go to school. At the moment he leaves the house he looks at the clock in the mirror. The clock has no number indication and for this reason the boy makes a mistake in interpreting the time (mirror-image). Just assuming the clock must be out of order, Matthew cycles to school, where he arrives after twenty minutes. At that moment the clock at school shows a time that is two and a half hours later than the time that Matthew saw on the clock at home.

At what time did he reach school?

Imagine that you need to put a coin into an empty bottle and then insert a cork into the neck.

Is there a way to remove the coin without taking out the cork or breaking the bottle?