Delete Rows With Duplicate Data VBA - vba

Question

I am struggling with something that should be fairly straightforward, however, I have read at least 15 methods of doing this and cannot seem to get it to work.
Here is a sample dataset:
9:30:01 584.7
9:30:01 590
9:30:01 595
9:30:02 584.51
9:30:03 584.62
9:30:04 584.44
9:30:05 584.05
I only want one row per second, so of the first 3 rows, only one needs to stay. I don't care if it is the first or the last, but the code I have been using keeps the last, 595 in this case.
The way I am doing it is with a for loop that clears the contents of the row that has the same time as the row below it. I then sort the entire range.
I imagine there is a simpler way to simply delete the extra row from the get go. However, when I use delete on the range, instead of clear, it won't remove all of the duplicate rows.
Here is what I want the data to look like:
9:30:01 595
9:30:02 584.51
9:30:03 584.62
9:30:04 584.44
9:30:05 584.05
I need this to happen for the entire sheet. The time is Column B and the values are column C.
Here is the code I am using,
LastRow = ActiveSheet.UsedRange.row - 1 + _
ActiveSheet.UsedRange.Rows.Count
For RowNum = 2 To LastRow
If (Range("B" & RowNum) = Range("B" & RowNum + 1)) Then
Range("B" & RowNum).EntireRow.Clear
End If
Next RowNum
Range("A2:C" & LastRow).Sort key1:=Range("B2:B" & LastRow), _
order1:=xlAscending, Header:=xlNo

Answer 1

Don't loop. Use RemoveDuplicates. Way faster than any loop. One line of code.
Sub test()
ActiveSheet.Range("B:C").RemoveDuplicates Columns:=1, Header:=xlNo
End Sub
Edit: screenshots
BEFORE
AFTER
Edit: Does not work in Excel 2011 for Mac (go figure).

Answer 2

This should do the trick:
Sub jzz()
Dim i As Long
For i = 1 To Cells.SpecialCells(xlLastCell).Row 'loop from row 1 to last row
If Cells(i, 1) <> vbNullString Then 'check if something is in the cell
If Cells(i, 1) = Cells(i + 1, 1) Then 'check if cell is the same as next cell
Cells(i + 1, 1).EntireRow.Delete 'if so; delete
i = i - 1 'go back one row
End If
End If
Next i
End Sub
Another option is to go from the bottom up, like so:
Sub jzz()
Dim i As Long
For i = Cells.SpecialCells(xlLastCell).Row to 1 step -1'loop from last row to row 1
If Cells(i, 1) <> vbNullString Then 'check if something is in the cell
If Cells(i, 1) = Cells(i + 1, 1) Then 'check if cell is the same as next cell
Cells(i + 1, 1).EntireRow.Delete 'if so; delete
End If
End If
Next i
End Sub
what you prefer to use if personal. Please consider the answer of teylyn as well, in this situation, it is very usable.