Anyone found an answer to the slow time m/c backups?

Question

This slow back up problem with Time Machine has affected my Mac Pro work station since I installed Mountain Lion a few weeks ago. This is not a wireless problem as my time m/c is connected via a usb lead.
I decided to replace my 4 year old 1TB WD HD which I have been using as Time m/c since December 2008 as this drive had filled up quite rapidly since installing Mountain Lion, and I replaced it with a new 1TB WD HD two days ago. This did not resolve the slow back up problem, but eliminated a possible cause of slow back-ups.
I wondered if Time m/c was rewriting files as it used up quite a bit of space on my old HD?
The time m/c HD pauses for some time during backups, and will take well over 30minutes to backup a few megabytes of information.
Currently I am backing up my work whilst working, and I now cancel back-up on shut down as it takes so much time to back up to file vault.
The 1TB WD HD I am using for Time m/c contains all of my data from the two hard drives in my machine, but a check of the volumes of my HD's bares little comparison to that shown by the volume on Time m/c.
A 2011 Macbook Air which had Lion installed on it when purchased, and has now been updated to OSX 10.8.1 does not appear to have problems backing up to a 500GB Seagate portable drive. Although my 2010 Macbook Pro now updated to OSX 10.8.1 does appear to be slower backing up to a WD My Book 500GB HD.
Hope some one can solve this problem as I am baffled.

Answer 1

If you have more than one user account, these instructions must be carried out as an administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad. Click Utilities, then Console in the page that opens.
Make sure the title of the Console window is All Messages. If it isn't, select All Messages from the SYSTEM LOG QUERIES menu on the left.
Enter the word "Starting" (without the quotes) in the String Matching text field. You should now see log messages with the words "Starting * backup," where * represents any of the words "automatic," "manual," or "standard." Note the timestamp of the last such message. Clear the text field and scroll back in the log to that time. Post the messages timestamped from then until the end of the backup, or the end of the log if that's not clear.
Post the log text, please, not a screenshot. If there are runs of repeated messages, post only one example of each. Don't post many repetitions of the same message.
When posting a log extract, be selective. Don't post more than is requested.
PLEASE DO NOT INDISCRIMINATELY DUMP THOUSANDS OF LINES FROM THE LOG INTO A MESSAGE. If you do that, I will not respond.
Some personal information, such as the names of your files, may be included — edit that out, too, but don’t remove the context.