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The simplest answer would be to put a row in for daily totals and just count on that row.
alternatively you could check each column and sum up the results
Assuming that Hours A Day 1 data is in cell B3
=(SUM(B3:B7)>0)+(SUM(C3:C7)>0)+(SUM(D3:D7)>0)+(SUM(E3:E7)>0)+(SUM(F3:F7)>0)
When the check for each column is false the value is 0 when the check is true the value is 1.