The accounting utilities (e.g. GNU's implementation) track user activity and provide a number of tools to report on it; for example,
will list the last commands executed, and
root) will provide an activity summary.
To show the amount of time a given process ran, do something like
sudo sa | grep chromium
This will output a number of values:
5 6781.67re 3.78cp 0avio 265418k chromium
4 4521.35re 0.00cp 0avio 176024k chromium*
The first column is the number of times the given process ran, the second is the number of minutes the processes ran in total (which may be simultaneous). The line ending with
* summarises processes which forked without executing another binary. Since browsers tend to execute multiple processes simultaneously, the starred instance represents the extra processes used; you can get an idea of the real time spent by subtracting the values in this case.
These values are aggregated over all users, so they're only really usable for your purpose if you're the only user on your system.