Do triathlons have finish times?

It depends on the race. Many have an estimated schedule. Normally if it is a hard and fast cut off they will mention it in the rules or somewhere on the website.

Of the sprints I have done (more than 25) I don't think any had a strict had to finish by xxx time rule. This can be dependent on location, Race Director, and permits issued by town or area.  Only race I know that has hard and fast time cut off is Ironman distance races.

Enjoy your journey to your first triathlon!

Often the finish times are for scheduling of the awards ceremonies. If you're finishing after 8:55 you clearly didn't podium. There have been many races where people are still finishing their race after awards have been distributed.

I looked up the distances for your race (swim: 375m, bike: 10km, run: 2.5km). This race is half of a standard sprint distance. Average times for a sprint are under 2 hours. I'm certain that you'll be fine with a 1:55 window. Good luck, it's gonna be fun, and addictive. 

If you did every event really slowly:

Swim  375m at 3 minutes/100 = 15 minutes

T1 = 5 minutes

Bike 6.2 miles at 10.5 mph = 35 minutes

T2 = 5 minutes

Run 2.55 miles @ 3.2 mph = 45 minutes

1 hr 45 minutes

Train and do the race and you will laugh at the times I suggested.

Yes. Technically you'd receive a DNF.
But, as someone pointed out up above, you'd need to be very slow at all disciplines, and pretty much stroll the run section to come close to the cut-off.

Don't stress yourself out over the cut-off times. You have plenty of time to train and get used to OWS, and the bike-to-run feeling.
I recommend a few brick workouts, where you bike then immediately go for a run. It's a very strange feelng (jelly legs) if you're not accustomed to it.

^^^ That's a great (i.e. funny) story!  

yeah you have to adjust pace/intensity for a brick. i couldn't imagine doing a brick in a gym with poor airflow.... that would be like the peak of summer.  don't focus on combining workouts if your race isn't for a while, and instead just focus on each by itself.  

My guess is that's a typo - no way they expect everyone to finish in 45 minutes.  If you look at the results for that race from previous years, you can get a better idea of what reasonable times might be.

A few years ago someone on this board suggested that if people are worried about cut off times then they should train more to make sure they are ready to race. 

It wasn't me, by the way.

To answer the question in the subject line:  Yes, triathlons have finish times.

When you cross the finish line

They record your time.  

That is your finish time!    

You are probably correct that they will not credit you with an "official finish" if you aren't done by 8:55 after starting at 7:00.  Why do they do this?  Several reasons.  One is to be fair to race officials, staff, and volunteers.  Could you imagine the response to asking the city for a permit to close the street for a race but you won't tell them how long the street might be closed?  Another is to be fair to all participants.  Imagine how volunteers might be assigned if the race directory has no estimates for finish cutoffs.  You could be done and waiting for a medal and post race food being served by two overworked volunteers while 50 other volunteers are still out on the course serving one participant.  Similarly, how long will you hang around to be awarded your first-place-in-division trophy if they won't start the awards until everyone is done but nobody knows how long that will be.  It is also fair to you as an individual participant.  You saw the information about the cutoff and you're doing the right thing, asking questions to make sure you aren't the athlete holding everyone else up.  As a participant, I have a responsibility to train and prepare myself to complete the race within the allotted time.  If the 1:55 cutoff makes me nervous, I'm going to train to be absolutely sure I'll finish under the limit.  

Lest anyone think I'm a FOP elitist who only believes the fast people should be out there racing, I'm a MOP'er.  I have a lot of respect for people who still show up to race knowing that missing the cutoff is a real possibility as they're putting it all on the line every bit as much as the guys racing for first place.  

Go have fun training and racing!