Is it ever better to push your bike up a hill during a race

I noticed that it takes a ton of energy to climb a steep hill. Im doing
a duathlon comprised of 8 kms of running and 22 kms of mountain biking.
the fastest time will be a little over 2 hrs. i guess you can recover
during the downhill part but i could see myself burning up all my
energy on this hill that takes about 20 minutes to walk. there are also
5 mystery events which will be mental challenges which will give more
recovery time.