var startDate = new ISODate("2017-10-01")
var endDate = new ISODate("2017-10-31")
var startUnixTime = startDate.getTime() /1000 // convert date to time
var endUnixTime = endDate.getTime() /1000 // convert date to time

db.PermanentBookings.aggregate([
  {  $match: {
        $and:[
            { init_time: { $gte: startUnixTime, $lte: endUnixTime }} ,
            { city:"Madrid" }
        ]
     }
   } ,

   { $project:{
       duration: {
            $subtract: ["$final_time", "$init_time"] },

       week: { $week: "$init_date" } }
   }
])