At first, I thought this was a joke. But then, the writer is actually quite serious in asking where algebra is used in our everyday lives. And furthermore, this was written on the Washington Post, so it can't be a spoof (can it? :)).
Other than the fact that there are almost an infinite number of examples, the fact that this can even come up reflects the lack of not knowledge, but awareness of the things we take for granted, and thus, ever realize that we need them. This is true not only for algebra, but many aspects of physics as well. Many people think physics is only high energy/nuclear/string theory, without realizing that atomic/molecular and condensed matter/material science are also areas of physics that directly impact our lives every single day. Many people dismiss Special Relativity and General Relativity to the realm of exotic physics without realizing that we make use of those theories every time a GPS system is used. And let's not even start with quantum mechanics.
I suppose it is good that the writer actually ask such a question. At least, people can write in and tell her directly where algebra is used all the time. Hopefully, others who read the article will also come to a self-realization of how much we depend on algebra.
And oh, if she needs examples:
1. computing of one's interest amount in any financial account/credit.
2. when someone asks how long will it take to get some place that's such-and-such a distance away.
3. when you add, subtract, multiply, and divide a number or quantity (which should cover everything, shouldn't it?).