Running Total Based On Criteria

I would like to know if it is possible to have a cell calculate a running total based on previous data as soon as you enter new information. The spreadsheet is a log of suspensions. Relevant columns include the student's name, date, and length of suspension (in days). For example, if Column A= Name (could be separated into first and last name if necessary, or merged into one column), B= Date, C=# of Days, D= Reason and so on, can Excel add the number of total days of suspension for all violations as soon as a new record is created? (If a student has already been suspended for one day, then gets suspended a month later for something else for three days, can excel tell you immediately how many days that student has been suspended total?)

This is actually a question from my mom, who asked me to help her, and who told me that a former coworker's wife had created a spreadsheet that could do this. Unfortunately, that spreadsheet no longer exists and they must recreate something.