The times are probably preserved as text.
SUM will disregard the text, so it will return 0.
One possibility is to change the text to a real time, but since the time is already in a format that Excel can understand as a time, we can do it in the formula:
The -- will force the text into a number and the SUMPRODUCT will iterate the array and sum the results.
With Office 365 we can use SUM:
Older versions will need to use Ctrl-Shift-Enter if SUM is used instead of SUMPRODUCT which will not require it in any version.