The Heathrow Express from Paddington reaches the airport in approximately 15 mins

https://www.scribd.com/document/1074920514/Getting-to-Heathrow-from-Gatwick-Easiest-Inter-Airport-Transfers-178501

The Heathrow Express from Paddington reaches the airport in about 15 minutes. It’s the quickest rail choice, however pricier than the Tube.