Midpoint of a midpoint, then what?
\(AB\) is 60 units long. \(C\) is the midpoint of \(AB\). \(D\) is the midpoint of \(CB\). \(E\) is twice as far from \(B\) as it is from \(D\) such that it is between \(DB\). \(F\) is four times as far from \(C\) as it is from \(A\). Find \(FC + DE\).
Note: This problem is taken from the Mathizen Question of the Day.