What are the distances represented by a minute of latitude and longitude?

If you assume that the world is a sphere, then the distance between a degree of latitude (N-S) is constant where ever you are on the globe. The distance between a degree of longitude (E-W) varies from the equator to the poles. It is the same as the distance between a degree of latitude at the equator, but is zero at the poles. A very rough calculation is that

longitude distance = latitude distance X cos(latitude)

so if a minute latitude is 1.15 statute miles then at 38 deg 15 mins (38.25 deg) it would be

1.15 X cos(38.25) = 0.9031 statute miles

and at 38 deg 16 mins (38.266 deg) it would be

1.15 X cos(38.266) = 0.9029 statute miles

a difference of about a foot.

Of course since the world is really an ellipsoid, the actual calculations are more involved. The cosine approximation works well for large scale maps covering a small portion of the earth (like a 1:24,000 topo for example)