Question

Two cities are due north of each other. One city has a latitude of 32¢ª45'12" and the second city has a latitude of 51¢ª12'45". Assuming that the earth is a sphere with a radius of 4000 miles, how far apart are the two cities?

Answer 1

Same longitude, so you can just use an arc distance: radius*(difference in latitudes).

Once you do that, calculate it with a better computer model, with real Earth radius. Choose any longitude you wish, as long as they are the same.
http://www.movable-type.co.uk/scripts/latlong.html

Answer 2

50 72 45 (the 72 is 60+12)
32 45 12
----------subtract
18 27 33

now being a navigator, I happen to know that a minute of latitude is a nautical mile so
I would say
18*60 + 27 + 33/60
= 1107.5 NAUTICAL miles

However do not tell you math teacher that :)
we have 1107.5 Minutes of arc
that is
1107.5/(360*60) = .051275 of the circumference of the earth
which is 2 pi r = 25132.7 miles
1289 miles
Those are LAND miles, not used in navigation.