Heathrow Express MAY take 15 minutes. The only time it was convenient for me and I decided to give it try, it stopped part-way to Heathrow and we just sat there. I'd have gotten to the airport faster and paid quite a bit less to take the slower train from Paddington, the Heathrow Connect. Since then I make a point to stay along the Piccadilly Line of the London tube and pay the least of all.