Or, more accurately, I'm going to make it to your house safely either way but I don't care if I get there in 5 minutes or 15 minutes because there is no real urgency. The urgency is gone. I can't get there in 5 minutes if you gave me a warp engine. The damage is already done. So I'm going to get some errands done that could help me save some time next time we're in an urgent situation.
I'll still drive safely and responsibly. I'm not stripping the tires for wagon wheels and cutting the brake line, I'm simply resetting the priorities because there is no more urgency. I can't be ready this time, but I might next time if I take some steps towards it rather than driving like a bat out of hell when it's already too late.
Also, it sorta makes me (the driver) a little more cognizant about how I got myself in a situation where I couldn't get to your house in 5 minutes when it was urgent. Hopefully next time you want me there in 5 minutes I'll be better prepared for it. No better time to be working at that than now! You know, rather than rushing off after something that was already a failure/disaster.