This callout calculates how much time has been spent on activities within an incident.

First thing I did was customise the incident entity to include an incident total time field which I made read only to protect the data.
Now all we need is a callout to total up the total time of the incidents.
I based this callout on incident resolution and created the following code.

using System;
using System.Collections;
using System.Diagnostics;
using System.Globalization;
using System.Reflection;
using System.Xml;
using System.IO;
using System.Security.Principal;
using Microsoft.Crm.Callout;
using Microsoft.Win32;

namespace DotNetDeveloper.Callout
{
/// <summary>
/// Summary description for CaseResolutionCallout.
/// </summary>
public class CaseResolutionCallout : CrmCalloutBase
{
#region constructors
/// <summary>
/// empty constructor
/// </summary>
public CaseResolutionCallout()
{}
#endregion
#region Public Methods
/// <summary>
/// PreCalloutReturnValue
/// </summary>
/// <param name="userContext"></param>
/// <param name="entityContext"></param>
/// <param name="newStateCode"></param>
/// <param name="newStatusCode"></param>
/// <param name="errorMessage"></param>
/// <returns></returns>
public override PreCalloutReturnValue PreSetState(CalloutUserContext userContext, CalloutEntityContext entityContext, ref int newStateCode, ref int newStatusCode, ref string errorMessage)
{
// only do this for Incident resolution
if (newStateCode == 1)
{
 try
 {
 // setup impersonation
 using (CrmService service =  new CrmService())
 {
  service.Credentials = System.Net.CredentialCache.DefaultCredentials;
   service.CallerIdValue = new CallerId();
   service.CallerIdValue.CallerGuid = userContext.UserId;
   // get total time spent on case
   CalculateTotalTimeIncidentRequest req = new CalculateTotalTimeIncidentRequest();
   req.IncidentId = new System.Guid(entityContext.InstanceId.ToString());
   CalculateTotalTimeIncidentResponse resp = (CalculateTotalTimeIncidentResponse)service.Execute(req);
   // update the case
   incident inc = new incident();
   inc.incidentid = new Key();
   inc.incidentid.Value = new Guid(entityContext.InstanceId.ToString());
   inc. totalincidenttime = resp.TotalTime.ToString();
   service.Update(inc);
  }
 }
 catch (Exception ex)
 {
  // error handling code
 }
}
return PreCalloutReturnValue.Continue;
}
#endregion
}
}

Obviously you need to add a reference to the base callout class and also to the MSCRM Service.
Associated Callout.Config.xml code
<callout entity="incident" event="PreSetState">
<subscription assembly="DotNetDeveloper.Callout.dll" class="DotNetDeveloper.Callout.CaseResolutionCallout"></subscription>
</callout>

Ok that done, upon running this callout you will find that the callout should works as expected and populate the totalincidenttime.
One activity I would test more than others would be the appointment activity, as the method provided by Microsoft calculates the incorrect totaltime for appointments ( I came across the problem and solution and posted about it in this earlier post here .