Anything is possible, so yes "it's possible".
However, you need to think about how much you can handle. It will come down to your available time and how your studies impact your ability to safely and efficiently perform your job as a truck driver. This includes getting adequate rest and being in a ready-state 10 hours after you shutdown for your break.
Good luck.
I agree with G-Town's points. It is doable, but I wouldn't recommend trying it during your first year out here. You want to be totally focused on learning this business during that critical first year. Every rookie driver I have ever met was completely surprised at how exhausted they were at the end of their work days, and then they only have ten hours to shower, eat, maybe do their laundry, or exercise a little and then sleep before they have to be back at knocking down some serious miles again the next day. After spending that first year learning as much as you can and attempting to be the best you can be at this, you may want to try taking just one course at a time and see how much time commitment it takes. Very few people even survive their first year out here, and an even greater number throw in the towel during their first three months. People get into this with all the wrong expectations and the reality of it is usually a real slap in the face for those folks.
So, if you are just looking for a way to make some money while also going to school, I think it is a bad plan. If you just enjoy educating yourself a little at a time for your own edification, then it is definitely a plan that could work. This career demands a lot of time. We work very long hours under sometimes very stressful conditions. You'll need to decide which is your priority, education, or trucking. If it is education, then forget about doing the trucking thing.
Here's another thought...you wouldn't be able yo do "online classes" at a tradional college/university...Only online ones. Reason being, at least at the college I attended, you need to go to compass for testing at two to three points through the semester.
My company has a contract with an online college to give us discounts but the courses are very limited. And honestly, as stated above, when I looked into it, I realized I don't have the time.
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Is it possible for truckers to start taking online classes while driving???