using System;

using System.Collections.Generic;

using System.Linq;

​

public class Program

{

    public static void Main()

    {

        //declare intervals

        var secondryIntervals = new List<Tuple<DateTime, DateTime>> {

                new Tuple<DateTime, DateTime>( new DateTime(2015, 03, 15, 4, 0, 0), new DateTime(2015, 03, 15, 5, 0, 0)),

                new Tuple<DateTime, DateTime>( new DateTime(2015, 03, 15, 4, 10, 0), new DateTime(2015, 03, 15, 4, 40, 0)),

                new Tuple<DateTime, DateTime>( new DateTime(2015, 03, 15, 4, 40, 0), new DateTime(2015, 03, 15, 5, 20, 0))};

        var mainInterval = new Tuple<DateTime, DateTime>(new DateTime(2015, 03, 15, 3, 0, 0), new DateTime(2015, 03, 15, 7, 0, 0));

        // add two empty intervals before and after main interval

        secondryIntervals.Add(new Tuple<DateTime, DateTime>(mainInterval.Item1.AddMinutes(-1), mainInterval.Item1.AddMinutes(-1)));

        secondryIntervals.Add(new Tuple<DateTime, DateTime>(mainInterval.Item2.AddMinutes(1), mainInterval.Item2.AddMinutes(1)));

        secondryIntervals = secondryIntervals.OrderBy(s =>s.Item1).ToList();

        // endDate will rember 'biggest' end date

        var endDate = secondryIntervals.First().Item1;

        var result = secondryIntervals.Select(s =>

                        {

                            var temp = endDate;

                            endDate = endDate < s.Item2 ? s.Item2 : endDate;

                            if (s.Item1 > temp)

                            {

                                return new Tuple<DateTime, DateTime>(temp <mainInterval.Item1 ? mainInterval.Item1 : temp,

                                                                     mainInterval.Item2 < s.Item1 ? mainInterval.Item2: s.Item1);

                            }

                            return null;

                        })

                            // remove empty records

                        .Where(s => s != null && s.Item2 > s.Item1).ToList();

        var minutes = result.Sum(s => (s.Item2 - s.Item1).TotalMinutes);

        Console.WriteLine(minutes);

   }

}