And NO, assuming all the lines are straight is NOT unreasonable, it is the only way that the problem could ever possibly have a solution.
Wow, you got so close to my point but still fell short! My point is that you cannot reach a solution without making assumptions that fundamentally alter the solution. Your math is correct if and only if your straight line assumption is true. It may be a reasonable assumption, but that does not mean it must always be an accurate assumption.
It depends on the store. There are places where the self checkout lanes are dysfunctional and end up requiring waiting for a checkout worker (who are usually understaffed) to come and scan a code to fix it.