A student leaving school travels 100 m East before he realizes he left his textbook in his locker. He heads back towards school, travels 30 m West, and then stops as he remembers he has a spare textbook at home. So he decides to just head home, walking 70 m East before he arrives at his front door. What is the... (a) overall distance (b) displacement ... of that student?

-- The overall distance he travels is (100m + 30m + 70m) = 200 meters.

-- His displacement when he arrives at his front door is

D = (100m East) + (30m West) + (70m East)

D = (100m + 70m)East + (30m)West

D = (170m East) + (30m West)

D = 140 meters East

It's interesting to notice that his displacement is 60 meters shorter than the distance he walked.  

That's because there's a stretch of 30 meters somewhere in the middle that he actually covered three times.

Two of those times added to the distance his shoes covered (2x30m=60m), but they cancelled out of the displacement.

His front door is 140 meters East of school.  He walked 60m farther than that, going back and forth over the 30m piece.

the answer to this is proletariats.

hope this : )