I just landed at LAX and the flight attendant (who had a slight Latino accent, but was a native or near-native English speaker) gave the last announcement:
"As we prepare to land please have cups and other items ready to throw away, as we're going to make one last pass through the cabin at which time." Full stop.
There were several such utterances during the flight which ended with "at which time," each of which was clearly meant to signify "at this time." Is this a common usage in a variety of English I'm unfamiliar with, or is it more likely to be this one speaker's quirk?