42 Points

From the 2007 Australian Maths Competition:

There are 42 points P_1, P_2, ..., P_{42} , placed in order on a straight line so that each distance from P_i to P_{i+1} is  \dfrac{1}{i}  for 1\leq i\leq 41. What is the sum of the distances between every pair of these points?




From the 1998 University of Waterloo Fermat Contest:

Three rugs have a combined area of 200 sq m. By overlapping rugs to cover a floor of area 140 sq m, the area which is covered by exactly two layers of rug is 24 sq m. What area of floor is covered by three layers of rug?