The cores are doing separate tasks, each core is doing its task at 2.4GHz. That way you can run more tasks without making the system slow down, but the system wouldn't be faster running a single task.
Crashman's statement is absoloutly correct. But with that being said; what is true is that you can give an application an "Affinity" to one CPU core or the other.
Should you set your system up to use "Affinity", you can have one task/application (let's call it application A)being executed say only on CPU 1; and all other applicatins running on CPU 0. So the net effect is that "Applicagtion A" has all the resources of CPU 1's capacity. Now, this doesn't say anything about common memory useage or access to disk drives and the such; but; presuming "Application A" can effectively use "ALL" the resources of CPU 1; then it should complete faster than running "Application A" on a single cored CPU of the same frequency.
I can see using "CPU Affinity" for such things as Electronic Circuit modeling; validation or things like that.... or perhaps assigning a Game to CPU n.... but outside of that.... I can't quite figure out why a "Home Abuser" would ever consider using "CPU Affinity."
Hope this helps.