“Would you mind covering for me while I'm out?”
You're going to take a vacation. You need someone to do your job for you while you're on your vacation. You ask your coworker this question.
Would you mind covering for me while I'm out?
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"Would you mind ___ing?" is a polite way to ask someone to do something.
You can use this in business or personal situations when you're asking someone to do something that you expect them to agree to. It should be an easy request. If you need to ask someone to do something more difficult or inconvenient, one way to ask is:
Is there any way you could cover for me next week?
To "cover for" someone means to do their job for a short time while they're out of the office:
Hey, I need to run to the post office for a few minutes. Can you cover for me?
To be "out of the office" means that you aren't at work.
When you're talking to someone about going on a vacation or taking a sick day, you can sometimes just say "I'll be out." For example:
I'll be out next Friday, so can we schedule it for Monday instead?