The Rams showed their hand quickly in free agency Tuesday, and if things go the Rams’ way, it could prove to be an impressive hand at that.

Less than three hours into the free agency period, the Rams had landed tight end Jared Cook of Tennessee and had visits lined up with offensive tackle Jake Long of Miami and safety Louis Delmas of Detroit.

Cook, widely considered the best tight end on the market, agreed to a five-year deal with the Rams, who won a tug-of-war for his services with free-spending Miami. The deal is worth $35.1 million, including $19 million in guaranteed money. Incentives could raise the overall value of the deal to $38.5 million.

It didn’t look like the Rams had much of a chance to land Cook in the days leading up to the start of free agency and even Tuesday morning.

But the Rams closed strong, adding a speed element to their receiving corps. Cook was a third-round draft choice by the Titans in 2009, so spending his first two seasons with Jeff Fisher as his head coach in Nashville obviously helped the Rams’ chances.

Cook, 25, has wide receiver speed (4.49 in the 40) at 6-5, 248. He’s not much of a blocker and spent a lot of time in Tennessee lining up in the slot. Cook’s statistics in the NFL have yet to match his athletic ability, but the Titans have hardly gotten stellar quarterback play lately. His best season was 2011 when he caught 49 passes for 759 yards — 15.5 yards per catch, which is a good average for a tight end.

One of the main focuses of the Rams’ offseason game plan is to get faster and more explosive on offense. Adding Cook to the mix helps that cause. If the Rams add a speedster such as Cordarrelle Patterson or Tavon Austin in the draft at wide receiver, they would have a young corps of pass-catchers with plenty of potential: Cook and Lance Kendricks at tight end with Chris Givens, Brian Quick and Austin Pettis back at wide receiver.