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Default Index if conditional sum equals a value.

I have several columns of data. Column A is names, column B is hours, column
C is dates.

I'm looking for a formula that returns the date when the sum of hours for a
person (from a list in the range G2:G8) reaches a certain point (the number
in E1).

Currently the list is sorted by date in the hope that it will simplify this
problem.
 
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