need some training advice

ok folks, i think i need some help:
I bought my first bike a few months ago. I ride a hardtail mtb and dont go offroad at all but usually ride the hills here in Jamnaica. These rided are usually 10-20miles, half being uphill.
I have approximately 280miles on the bike and always ride sat and sun mornings. i feel I consistently get stronger and faster going up the hills.
I also have been spinning two to three times per week and also feeling stronger as each class goes on.
So a friend says, you have to ride the flats as well as the hills to become well rounded, so over the past three weeks I have done this with him. It is a 10mile course and I can hardly finish the first lap. I usually hit the first part (5miles very strong) and somewhere in the last 5 my legs just get burnt out.
HELP I want to get better.
He says I am spinning too fast and being that my cardio is already strong I am just burning my legs out and that I should be pushing a harder gear and slow the cadence down.
Any advice would be appreciated.

Are you riding the flat on a road? Do you only ride on weekends?

I guess I have two thoughts.

One, you could try spinning a harder gear, and see how it works for you. If you like it, then you've learned something. Sometimes, though, friends you ride with make suggestions based on their bodies, and their suggestions aren't so helpful for us.

But, you've only been biking for a few months, it seems, so I'm guessing you're still building your biking muscles and stamina. I'd just keep riding and having fun, up and down hills, on flats, whatever is fun and feels good and challenging.

I got a heart monitor last summer, and watching my heart rate made me a bit more aware of how hard I'm trying at various times; if I'm already trying and riding hard, and there's a hill, I just don't have another 10 beats a minute in me. So if it's in your budget, looking at a heart monitor may reassure you that you're getting more fit? Similarly, a bike computer might help you see how fast you're actually pedaling, and how you feel pedaling at different rates.

And then, if you're riding on the road, and it's in the budget, you could always use it as an excuse to add another bike! :)