This question has been coming up frequently. Why does the eclipse path travel from west to east instead of east to west?
The simple answer is that the Moon is moving faster in space than the spinning Earth.
You say: What? The Moon takes a month to complete one revolution around the Earth and the spins around once each day. How could the Moon possibly be moving faster?
Imagine two racers. Each will be given a track to race on that is circular and goes around the same center point. (Makes it easy for us to watch them both.) So one racer gets the inside track and the other gets the outside track. And lets say the inner track is four times shorter than the outer track. If both racers run at the same speed it makes sense that the inside track racer can get around the track four times while the racer on the outside finishes just one lap.
The two racers can be thought of as the Moon going around the Earth and us sitting on the surface of the Earth spinning about the center once a day. So how big are the two tracks and how fast are we moving?
Earth track: Earth radius is 3959 miles (average). The length of the "Earth track" is the circumference which would be 24,875 miles. That is a long track and we "run it" once each day. So let's divide that number by 24 hours to learn the speed in Miles Per Hour. The answer is 1036 MPH. This is the speed of the Earth's rotation at the equator. You don't feel it, Earth is a lot bigger than us. Kind of like sitting inside a moving car, you don't feel the movement unless the road is bumpy, you change the speed, or you open the window.
Moon track: The Moon is 238,402 miles away (average). That makes the length of the "Moon track" 1,781,704 miles. And the Moon makes it around that track once every 29.53 days for an average speed of 2514 MPH.
The Moon is moving two and a half times faster than the Earth is spinning! As a result, the Moon's shadow crosses from the West to East, the same direction the Moon is moving relative to the background stars.