Timesheet adding rows

Hello,

I'm trying to work out a formula so that I can hand off my timesheet to a new manager and have it work correctly. Right not I sum a row of totals ( = SUM(B2:B20) ) and take out any shifts that aren't being worked. What I want is for the sheet to only add the number of hours if there is a name in the adjacent cell. So something like = IF(ISTEXT(C2), SUM(B2:B20)) but I want to treat each cell individually.

So, is there a way to create a loop that iterates through each line and only adds if the cell is blank?

so if

8:00 - 12:00 | 4 | Alicia
8:00 - 12:30 | 4.5 |
9:00 - 1:00 | 4 | Brent
Total hours | 8 |

I'm hoping this makes sense.
Thank you!