Are they all on the same straight road?
If they are and the library is between his house and the school then the distance from the library to the school is 4/5 - 3/8 = 32/40 - 15/40 = 17/40 miles.
If they are on the same road but in opposite directions from his house then the distance is 3/8 + 4/5 = 32/40 + 15/40 = 47/40 miles.
If they are not on the same straight road then we cannot work out the distance exactly but it must be between 17/40 and 47/40 miles as these are the best and worst case examples.