Our Moon in its elliptical orbit travels fastest when it is?

At its Apogee

That is when it has Earth beween it and The Sun

And getting a pull of Gravity from both

The Moon is basically shortening its trip

An Interesting time too, when we can get Supermoons and Lunar Eclipses

All orbits, regardless of what is being orbited, is when the satellite is nearest.  The general case is called periapsis, or for the Moon going around Earth it is perigee, which occurs every 27.32 days.  Kepler's Second Law, published in 1608

Closest to the Earth.

Read Kepler's Laws.

It travels fastest when it's closest to the earth.  As if moves away from the earth it slows down.  As it moves back closer to the earth it speeds up.  At its perigee, the closest point to earth, it's moving the fastest.