Can’t sum numbers by name from separate worksheets.

This problem is beyond my experience. Any help is greatly appreciated.

I’m using Excel 97. Please refer to the provided screenshot.
To make this easier to explain and grasp, I set the screenshot up to show a stylized version of three separate worksheets in a workbook.

Present situation:
Sheets 1 and 2 contain names in column A, and hours for each name in column B.
Some of the names in Sheet 1 are in Sheet 2---highlighted in bold print but with different hours from Sheet to Sheet.
Some of the names in Sheet 2 are not in Sheet 1.
The names are not in any order from Sheet to Sheet.

Desired situation:
I’d like to have Excel automatically list the names in column A Sheets 1 and 2, in column A Sheet 3 but not repeat a name.
I’d also like for Excel to sum the hours in column B for each name in Sheets 1 and 2 and enter the total next to the name in column B on Sheet 3.

Can this be done, and if so, how on earth can I do it?