Got asked about my answer to this eternal question to all math instructors today, "When am I ever gonna use this?"
My experience as a second career teacher really helps with answering this question. I was an engineer for ~12 years prior to teaching. I have seen how the economy has changed from the late 80s to now and what has been working.
I always tell them how the world has divided into those that can solve problems and make a good living - skills learned from math. And those that cannot solve problems, and typically don't make big money.
I also stress that time is not the factor - so taking time is ok - it is tenacity, and conceptual understanding. I also take the time to talk about the need to learn because no one asks for your Algebra 2 grade, but if you cannot solve problems you are the first to get by-passed for promotion, first to get stuck with the crap jobs, and the first to be laid-off.
I take time to talk about how the world has changed from the 1950s, 60s, and 70s. How the world has become small and the economy global. Meaning every job can be done everywhere (almost) and a lot of the world wants what we have here in the USA, and will work really hard for it. So we have to work hard and smarter, we have to be good problem solvers, thus we need the math.
Finally I talk about a couple of my courses in engineering, where I spent the entire semester learning how bolts broke and sheared. Then I came into the world and always looked up bolts instead of calculating the size. I explain it is understanding how the world works that makes us ready to tackle the tough problems, so the engineering courses are showing I could learn, adapt, those are the skills I needed. It gave me context for the problems I encountered!
I tell them that one of my first jobs was at Hormel working with SPAM - engineering/college did not teach me how to seam SPAM cans -- but those engineering courses and MATH courses helped prepare me to solve problems. So when the machines did not work I knew how to THINK about the problem. I also made a good living!
It does not matter the students eventual career, the better problem solver they become, the more employable they become! "The more math you take, the more money you make!" (an SA catch-phrase at school) I really do love when my students ask "When are we are gonna need this?"