The question might seem basic but it is actually quite more complicated that you think. Without knowing their specific procedures I can give some basics on departures (initial departure separation)
If someone is departing runway 33, the aircraft departing runway 1 cannot start it's takeoff roll until the other aircraft is across the intersection and vice versa.
You need at least 15 degrees course divergence if you plan on putting the two aircraft within 3 miles. So, between 33 and 1, you have 40 degrees. They can both go straight out and right away you have the 15 degrees. They wouldn't let them go if they were on the same route obviously.
Most aircraft at DCA are "Category III" (not to be confused with weather...this is for same runway separation). So, if two are departing the same runway, the second one can technically start it's takeoff roll as soon as the first one is 6000 ft down the runway AND airborne...we as controllers do this...not the pilot. However, you can't send a 737 up the butt of a slower type...you still need either 15 degrees, 3 miles, or visual separation. (Yes, whether or not we can see from the tower determines what we can and can't do)
Those are just basics...within the rules you can get them pretty close working at a tower as this is just the INITIAL separation. It's fun too
There are other rules depending on runway configuration, how far the runways are apart from each other, whether or not they are staggered...etc. There's quite a bit to it.