Lugging our backpacks, it took us the better part of 10 minutes to reach the vicinity of the mound.
Could someone please paraphrase "the better part of 10 minutes"? and in what else other situation "the better part of " can be used?

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@codin28
Thank you very much for your easy to understand and concise reply.

@Xan_Amar
Thank you very much for your reply,which interested me.It is a great asset to know that "the better part of" can function in space and emotion(or abstract thing). I will keep that in my mind for possible uses in the future.
By the way,your examples led me to another question to ask of you,may I?
Suppose you are carrying a whole cake and stumbles on something,and the cake falls off to ground. It is damaged partially heavy,partially light. You discard the heavily damaged part, but you keep the partially damaged part. In this situation, what's left of the cake can be called the better part of the cake even if it is less than half the original.
Thanking you in advance.

P.S.
I wonder if I could make myself understood.
Any correction or refining would be appreciated.

@Xan_Amar
Thank you very much for your assistance.
I wrote down what I got from your answer in my words so that I can digest your thought better. If you disagree any of them,please let me know.
First,"The better part" simply doesn't mean the cake I was able to save.
Secondly,the cake I was able to save is referred to as a whole.
Thirdly,the better part of new whole cake(the whole part) is still edible.
Lastly, so "the better part of " used above means more than half or most of it despite it is less than half the size of the original whole.

P.S.
The story is just my wild imagination !