How to use the word "better"

[RickGove]

Dear Teachers,

I am trying to explain why this sentence is wrong: "I wonder if a monkey could better run the TTC?"

I think it has something to do with better being used as a future tense or something like that. The more I read it, the more correct it sounds though, so please help me here.

*By the way the TTC is the Toronto transit commision.

[Mister Micawber]

'Better' is OK in that position, so it is not wrong, but it usually follows the clause: 'could run the TTC better'.
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Native English teacher at Mister Micawber's