2440.13 – Driving to Nirvana

Tags:Problem Set 7GeometryAlgebra

We were driving to Nirvana and I fell asleep. No, I was not driving, just eager to get there. So, when we were halfway there I fell asleep. When I woke up, the distance we still had to go was half as far as we went while I was asleep. For what fraction of the trip was I asleep?


Let yy be the whole trip and xx be the part that I slept through. Then the portion after I woke up is x/2x/2. The half of the trip after I went to sleep is x+x/2=3x/2x + x/2 = 3x/2. Therefore the whole trip, being twice that half, is 3x3x.

Thus, y=3xy = 3x so x=y/3x = y/3 and it seems I was asleep for a third of the trip. Did I ever get to Nirvana? That is another story and will be told another time.