I do 20 miles each way with a reasonable amount of climbing. I do it 5 days a week occasionally but not every week, so between 3-5 on average. I also ride at the weekend. I head down to the coast on the return journey so pretty much always have a strong headwind home.
Doing a 60 mile round trip 3 times a week would be perfectly doable though by 5 days on the trot would be a killer.
60 miles is pushing it a day, and 15mph what you riding a unicycle?
It is if you're going to hammer it all the time. 15mph average is lower than I would expect on a road bike though. Think my average last year for just under 6000 miles commuting was 16.5mph, that's including winter where speed does drop a fair bit.
Leave what you can at work, the less you have to carry the better. In summer everything I need goes in my back pockets and I do a clothes changeover the days I drive. In winter I use a waterproof rucksack as I'm happy being a bit warmer, have another light at a higher level and need a bigger range of kit with me.
But yes its perfectly doable.