I'm going to suggest that sound is whine rather then a "whrrrr". If I'm correct, there's probably no problem. My 790 used to whine in reverse (but I cannot recall if my old 670 did, even though it was quite similar to the 790).
Gears do that. Backlash (a measurement to ensure proper mesh of the gears) is checked in the primary driven direction. If the backlash is off (even if in allowable specs), those gears may be noisy (the "whine").
Older pickups and other trucks (up to the 1970's, Id guess) with manual transmissions used to be quite noisy in this regard.
However, I'm guessing that's what you hear...without hearing it myself, I can't say for sure. I suggest you ask the person you bought it from, or a local Deere dealer.