Try this. Change the the type of conversion you are preforming but use the same numbers. You get the same thing! No, the calculator is not broken. Both of the conversions are the same operation.
Lets start with miles/hour :
X mi/h -> min/mi
X mi 1 h X mi
---- * ------ = ----
h 60 min min
1 X mi min
- / ---- = ----
1 min X mi
Now lets go the other way
X min/mi -> mi/h
X min 1 h X h
----- * ------ = ---
mi 60 min mi
1 X h mi
- / --- = ---
1 mi X h
Now if you follow this far just take out the units and you get the same equation for both!
X 1 X
- * -- = --
1 60 60
1 X 60
- / -- = --
1 60 X
There you have it. Just devide what ever your are trying to convert into 60.