Simple math: partitioning the time between two DateTimes

[J. David Blackstone]

 Given two DateTime objects as input, and an integer $N, I want to 
partition the time in between them into $N equal intervals and return 
an array of $N + 1 evenly-spaced DateTimes that begins with the first 
input DateTime and ends with the last input DateTime.

 The straightforward way of doing this would seem to be to subtract 
the two DateTimes, divide the resultant interval by $N, multiply and 
add repeatedly.  But it doesn't work because DateTime::Duration just 
can't handle that kind of math.

 What's the right way to do this?  And what would it take to make a 
class comparable to DateTime::Duration that represents an interval of 
time that can actually be manipulated in this manner?

jdb