If I'm asked how long it will take to go 84 nm at 120 kts, I know that it's
about 40 minutes, but if an exact answer is required I don't see how I
could practically provide that without a calculator.

Whizwheels were the classic, calculators are acceptable.

I learned to fly in France in the mid-80's, and all student pilots were taught
to do these calculations mentally, using the "facteur de base" = 60/TAS. It
takes practice but works really well.