1990 Testdrive noise

I testdrove a 1990 Cherokee (manual everything - basic), 129K, $2600, 2nd owner, mostly good everything...with the exception of a whirring/humming noise coming from the rear of the vehicle in between accelerations...was disturbing...what could this noise be?...owner said maybe it was something called a differential....is this car still a good deal if this differential needs repair?....

...buying this car to drive cross country from California to Vermont...am I crazy?...or should I pursue....

No way to know without having someone who knows car mechanicals look at it. Maybe it is just low on oil; easily fixed. Maybe there's some bearing or bushing wear; will need to repair it eventually but it will probably get you to VT. Maybe things have worn enough to spoil the precise alignment of the gears. If that happens, you could have a tooth break on a gear and jam everything up. If that happens while you're driving, the rear end will lock up and skid. That can be pretty exciting and dangerous.

The differential is an essential mechanical unit and I wouldn't begin a long trip without having it checked out.