Grob Queen,
It was not my intention to "shout you down" but the idea that the tailwind will cancel out the effects of the headwind is potentially very dangerous. I have met many pilot who have clung to this mistaken belief right up to the start of their ATPL General Navigation studies.
My reason for providing my arguments in the form of a step-by-step calculation was to encourage you to try this for yourself. If you adopt this as a general principle you will probably find that you understand things much better. You might like to try it using the same scenario, but with a 35 kt wind. You will still find yourself about 17 minutes short of fuel. Can the aircraft that you fly, glide for 17 minutes from the altitudes at which you fly it?
If you now go back to your CFI and show him/her this thread, his/her reaction will probably be something along the lines of "but that isn't the question you asked me" or "I didn't say that", or possibly simply "Oh bugger, you caught me at a bad time, sorry".