If you travel west through 10 degrees of longitude along the equator, the distance traveled will be very different from the distance traveled through 10 degrees of longitude at 60 degrees north latitude. why?

When you travel θ degrees of longitud at a certain latitude, you are travelling along the arc of a circle. The radius R of that circle is decreases as you approach one of the poles: it is maximum at the equator, and zero at the pole.

The arc of circle is S =  R*θ. At 60 degrees latitud North, R is less than at the equator.