Assuming the run portion of the tri is a 5k... I think you are probably ok.

Usually when I am training for a sprint I will do 1 longer run and 2 short (speed workout) runs per week.

The long run is usually around 6 miles and the short ones are 3-4 miles.

Everyone is different and this is what works for me. It may or may not work for you. But atleast you have an idea of what someone else does.

Hope that helps...

One aspect that has not been mentioned is a high cadence through out the bike portion of your event. This will help ease your transition from the bike to the run. I usually try to increase my cadence by 10 to 15 percent before I get off the bike. For example I go from 90 rpms to 100-105rpms. This may help you.

As far as distance I would say that weekly I am running a minimum of 16 miles a week. One long run, one short tempo run and one mid distance mid pace transition run. long run is 6-8 miles short is 2-5 and mid is 3-4.

Hope this helps.