Suppose that |a−b|+|b−c|+|c−a|=20. What is the maximum value of |a−b|
Let a > c > b
Then
l a - b l = a - b
l b - c l = c - b and
l c - a l = a - c
So
l a - b l + l b - c l + l c - a l = 20
a - b + c - b + a - c = 20 simplify
2a - 2b = 20
a - b =10
So...the max value for l a - b l = 10
+145 
