Why is a solar eclipse of a shorter duration than a lunar eclipse?

The reason a solar eclipse is shorter and more elusive than a lunar eclipse is because of the relative sizes of the shadows of Earth and the Moon.

The shadow of the Moon is much smaller, so it takes less time for the shadow to pass over a given point on the surface of the Earth. However, the shadow of the Earth and the smaller surface of the Moon means that it takes longer for the Earth's shadow to pass over a given point on the Moon's surface.