What would BT do? (bike question)

What kind of gearing is on the road bike and how hard are the hills? I'd really be looking at using the road bike.

Well, if all else fails you could try your local bike shop.

I started training in January on my mountain bike.  I was living in the Texas Hill country and yes I was riding some very hilly routes.  

I was averaging 14.8 MPH on these training rides.  Going up hills was a killer.  I often would only get halfway up before I ran out of momentum and be forced to dismount and run the bike up the hill.  Coming down the hills was great on the mountain bike though.  I would tuck and hold and descend at speeds over 30 MPH.  So...for climbing hills a mountain bike is not a good option due to the extra weight and increased rolling resistance, but coming down hills the extra weight is a plus and the wider tires and steering made it handle well at top speed.

In race planning I looked at past finishing times and knew to be Age Group Competitive I needed to have a 3 hour bike split for 56 miles.  Running is my strength.  As a new triathlete I didn't have a chance of beating seasoned triathletes in the swim or on the bike, but I wanted to be close enough that I had a chance of running down some of the guys that do well in the swim and on the bike but struggle on the run.  

At 14.8 MPH I had no chance of catching any of the fast swimmers and cyclists so I bought a used TT bike.  The TT bike was much easier to climb hills with.  I never had to dismount the TT bike.  Even on the 1.4 mile long hill on my Saturday morning route that climbed 370 feet (6% grade over the 1.4 miles, but the first 0.625 miles is an 8% grade).  

On the mountain bike I would climb hills at 7.5 MPH.  On the TT bike I would climb hills at about 12.5 MPH.  I would be about the same speed on both bikes coming down the hills, but the mountain bike felt safer since it breaked better with the wider tired and was easier to steer.  Coming off the TT bike I would feel fresher than I would off the Mountain bike because the aero position would allow me to save energy.

The choice for me was simple.  I went with my TT bike.  I am surprised that anyone would prefer to climb hills with a mountain bike over road bike.  I am also surprised that anyone would run better off a mountain bike than a street bike.  You may just need to spend more time on the street bike to get used to it or you may have a fit on the street bike that is limiting what you can do.  

Note:  My TT bike is a "double" Cannondale Slice with 650c wheels.  My Mountain bike is a Schwinn "triple" with 26" wheels (size?).  The smaller wheels on the TT bike make hill climbing easier than it would be on 700c wheels.  The extra gears on the Mountain bike aren't enough to make it up the long steep hills. 

I am not sure what Distance you are doing in August, but here are some times to consider.

In a Sprint Trr with a 12.5 mile ride and 3.1 mile run you add add over 10 minutes to you bike time if you drop from 16-17 mph to 13-14 MPH.  Unless you can drop a 30 minute 5k run time to under 20 minutes by switching to a mountain bike your will have a faster finish time on the street bike

if you are doing an Olympic Triathlon the Mountain bike adds 20 minutes so again unless you can improve from a 60 minute 10K run to a 40 minute 10K then you are better overall on the street bike.

For a half iron distance you add 52 minutes to you bike time so unless the difference in you run time off the mountain bike is significant enough to take a 2-1/2 13.1 mile run down to a 1 hr 38 mins, your mountain bike won't improve your race time.

And for the full iron distance your mountain bike adds 90 minutes to you bike leg so unless you fresher legs can improve a 5 hour marathon time to a 3-1/2 hour marathon time, again the mountain bike isn't going to improve your over all time.

Your race isn't until August. You can make dramatic improvements on the hills in that amount of time if you're willing to work. You've got hills to work on, so get out there and do hill repeats. My favorite story with those is a long hill I couldn't make all the way up once, within a short time I was doing it 20 times in one session. 

I personally wouldn't mess with changing gearing until you've worked more on it. To say that bike is incapable of climbing as setup is incorrect  That's what people rode back then.  Just make sure everything's lubed up and working and ride the heck out of it. Have fun. 

ETA: I'm a fan of those older bikes. Cannondales are nice, gotta pic?

This^^^

I'm pretty sure I had this bike too. A Cannondale Criterium. In fact, I just retired it this past winter. It as a late 80s Alumnium bike, but I did manage to get a 9 speed wheel with a cassette in there instead of the 6 speed freewheel. Actually I went from 6 speed freewheel to 8 speed cassette, then 9 speed cassette. The first few times I had to remove my wheel it was very tight, but the chainstays did spread over time. YMMV

Mine also came with 42/52 (or 53) Biopace chainrings. You could swap that for something a little easier.

Mike bike is here. http://www.beginnertriathlete.com/Albums/Album/1512 I think there is a picture of the cassette.