ILL 1977 Problem 51

Several segments, which we shall call white, are given, and the sum of their lengths is $1$ . Several other segments, which we shall call black, are given, and the sum of their lengths is $1$ . Prove that every such system of segments can be distributed on the segment that is $1.51$ long in the following way: Segments of the same colour are disjoint, and segments of different colours are either disjoint or one is inside the other. Prove that there exists a system that cannot be distributed in that way on the segment that is $1.49$ long.