How to copy the contents from the sub files to the master worksheet based on the id?

Every Friday I receive about 50 excel sheets titled time utilization along with their id (eg: timeuti-1001, timeuti-1002, etc) from my classmates. Currently I am physically copy-pasting the details that they send. I would like to automate this task.
I am saving all the files in C:\timeutilization.

When I click on the ‘Reconcile’ command button in the mastersheet which is in the same folder. I want the macro to identify the student id from timeuti-1001 filename and for that particular student id I would like the macro to match it with the student id cell in the master sheet and copy the contents of the cell for that particular student id.

Eg: Student with filename “timeuti-1007” sends the details this Friday.
pic1.JPG
I would like the mastersheet to look like this:
pic 2.JPG

For every student it needs to update it based on their id. If an user has not sent the details let the row remain blank. Thanks in advance.

Every Friday it needs to run.. The Mastersheet should match the date from the system time and timeuti worksheet for each user.

Thank You Very Much.. It Worked..

I added a new column in my Mastersheet for student name. That is in Column A , and I moved Student Id to Column B.
The individual utilization sheet remains same.

Is this correct:

lr = master.Range("B4").End(xlDown).Row

For Each studentID In master.Range("B4:B" & lr)

    StrFile = Dir(path & "timeuti*" & studentID.Value & "*.xls*")
    If Len(StrFile) > 0 Then
        Set wbtime = Workbooks.Open(path & StrFile, , 1)
        Set wstime = wbtime.Worksheets("Individual-Utilization")
        With wstime
            Set finddate = .Range("A4", .Range("A4").End(xlDown)).Find(Date, lookat:=xlWhole)
            If Not finddate Is Nothing Then
                finddate.Offset(, 1).Resize(, 21).Copy studentID.Offset(, 1)
            End If
        End With
        wbtime.Close 0
    End If

I had some problems when I had my friends send me their timeuti files. Mostly they used to change the dates. It also lead to some problems when using the system dates.
Currently I am using a combobox infront of my Reconcile button. Is it possible for me to take the date from combobox and match it with timeuti file rather than the system date?

testnew.JPG

I tried changing the Date keyword to ComboBox, but it doesn't seem to work.

With wstime
            Set finddate = .Range("A4", .Range("A4").End(xlDown)).Find(ComboBox1, lookat:=xlWhole)
            If Not finddate Is Nothing Then
                finddate.Offset(, 1).Resize(, 21).Copy studentID.Offset(, 1)
            End If
End With

What do you suggest I use "Friday" as? Should I be changing the format?

I added the changes you suggested. I got an error "run-time error:91 Object Variable or With block Variable not set"

Thanks. This works..
You are the best..