What to say when you’re running late?

I left early for work, as usual. But there was a major traffic accident that delayed me 45 minutes. So I texted my boss to tell them I would be 45 minutes late. But the accident ended up only delaying me 15 minutes. We just so happen to be cracking down on tardiness at work, and we are in the process of starting to write people up. Should I show up at the 45 Minute delay that I talked about? Or should I stick to the 15 minutes that it ended up being? I feel like being delayed by a lot of time seems a lot more believable than being just slightly late, which seems avoidable.

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