This Answer has already been solved by sailor Steven Callahan who wrote the bestseller "Adrift, 76 Days Lost at Sea". If is a modern dingy it doesn't need to be that big, and depending on the sailing condition of the raft, to travel 500 miles it could take from 20 days by drifting alone to less than a week if rigged with a sail. As for the food, not much will be required because the ocean could provide lots of it. In the case of a raw tree beamed raft it is hard to tell how the currents will affect the rough non-streamlined surface of such a raft by slowing its speed and altering its course.
http://www-rohan.sdsu.edu/~cdorman/book_website/images/Adrift.jpg

In 1982, while attempting a solo crossing of the Atlantic Ocean sailing alone from the Canary Islands to the Caribbean, Callahan capsized during a great storm with his sloop and escaped in a small inflatable rubber life raft taking with him an emergency kit containing basic food, essential items such as navigation charts, a torch, a rudimentary rainwater collector and a copy of the book “Sea Survival”.

His raft drifted westward with the South Equatorial Current and the trade winds. After exhausting the food supplies, Callahan survived by eating the fish he speared that followed him across the ocean, the sailor also collected drinking rainwater from two solar still devices he rigged. He spent 76 days adrift, until the raft arrived close to the island of Guadeloupe, in the West Indies. During his ordeal, he faced sharks, raft punctures, broken equipment, and experienced deteriorating physical and mental condition.

Today Callahan is a self made naval architect and still enjoys sailing. During his surviving experience he wished for a rescue that never came, and realized the limitations of a traditional life raft. He considered how his needs could have been better served; a boat was needed to fulfill the function as or better than a life raft. Almost 20 years after the ordeal, he invented and designed the first FRIB (Folding Rigid Inflatable Boat) model, also called "the Clam", a folding rigid-bottom boat he developed based on his survival experience.

The Clam is a multifunction self-rescue utility dinghy, also designed as a lifeboat that allows the sailor to sail to safety. It offers the basics of what he found necessary while at sea. The raft has inflatable air compartments, watertight compartments and is covered by a canopy which protects sailors against the sun and rain. The bottom is made of fiberglass, to offer some protection from marine life below. One of the best aspects of the dingy is that a sail could be hoisted allowing sailors to navigate their way instead of just drifting downward. The raft measures 11.5 foot and stores as a 22 inch x 5 x 4 foot package. Callahan licensed to Hydra Nova Boat works who built the first 16 prototypes in two versions, folding and non-folding.

According to Callahan's account on his article "The Life Raft: Don't Leave Your Ship without It" from the "Ocean Navigator magazine":

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"..The last time I lost my boat, had I been able to beam reach, I could have shortened my drift from 1.800 miles to 450; had I been able to sail even dead downwind but increase speed to a moderate 2.5 knots, I would have been afloat 25 days rather than 76; had I been able to do both I would have sailed to safety in a mere six or seven days."
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The Folding Rigid Inflatable Boat also named the Clam, invented by Steven Callahan.
http://www.questionsforliving.com/senario_training/Clam_Canopy_Bow_Closed%20email.JPG