Catching Pic line from T3 towards Acton town. Which way is the quickest

[ACDC]

After clearing customs you follow the signs for the Tube. There are a myriad of travelators , however you pass the entrance of the HEX/ EL terminals to the left. I had a fleeting idea of taking that to T5 and then catching the pic. towards Acton town.
I decided not to, and the entrance to the tube is about a 5 min walk away. Then you have to take the lifts down.
My question is which is the quickest way

a) Take the free train towards T5 and tap in for the Pic. Line
b) Stick to what I did.

I noticed that the pic line was travelling a lot faster on both branches (Heathrow and Uxbridge.) For an old stock it felt like 45mph, I could be wrong. Is this is preparation for the new trains?

 

[sh24]

b) stick to what you did. by the time you've got down to the HEX platforms you would pretty much be on the escalator down to the Piccadilly line.

 

[Mawkie]

For an old stock it felt like 45mph, I could be wrong. Is this is preparation for the new trains?

45mph is the line speed for the Piccadilly Line. The 73 stock is perfectly capable of that (and should be doing that unless there is a temporary speed restriction in place).