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I would consider this unethical. The 33 cents per mile is for wear and tear on a motor vehicle no a bicycle. I like riding my bike though so I would rather just ride that extra day and not get the reimbursement.
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I don't think it unethical. 9 miles on bike tires, chain, bottom bracket, brake pads, etc. may not be the equivalent of a car, but it should be worth something. I'd say talk to your manager; my boss would allow me to do this & still reimburse me.