Very rarely are the hardback and paperback editions published at once. It is usually about 6-8 months after the publication of the hardback before the paperback is published, although it is sometimes possible to buy 'soft' hardbacks in the shops at the airport.
Sometimes it is longer than 6-8 months. I work on the book department of a major supermarket, and many of the current paperback chart books are the ones that were published in hardback form in time for last Christmas. It all depends on the publisher.