With the five-ringed Olympic flag now planted in Brazil, Rio de Janeiro — host of the 2016 Summer Games — is on the clock.

Suddenly four years doesn’t seem like much time to untangle the city’s chronically snarled traffic grid, shore up an inadequate public transportation system, make it easier to get to and from the airport and spiff up a decrepit downtown waterfront.

Then there is the national goal of prepping Brazil’s athletes to crack the top 10 in the medal count, a considerable leap.

“Time is an adversary but time is on our side. We are on time and going according to schedule,’’ Leonardo Gryner, the chief executive of the Rio 2016 organizing committee, said at a news conference before leaving the London Olympics.

But at home there are still concerns about potential cost-overruns, whether the city will get long-term benefits from the Olympics, and about people who are being evicted to make way for projects for the Games as well as the 2014 World Cup, which also will be held in Brazil.

Brazil got a bit of a head-start because it hosted the 2007 Pan American Games and more than half of the sports facilities that will be used for the Olympics are already in place — although some, such as the aquatics center, will need costly renovations.

The biggest challenge is expected to be getting the city — with its spectacular mix of sea views and lofty peaks — ready to handle hundreds of thousands of people for the Aug. 5-21, 2016 Olympics and the Sept. 7-18, 2016 Summer Paralympics.

Some 8,000 rooms of the three-star category and above are under construction and 9,000 more rooms are on the drawing board or in various stages of approval, but Rio is still expected to have a hotel deficit when the Games roll around.

Plans are being made to use cruise ships docked at the downtown port, which is slated for a massive renovation, to handle some visitors.

By 2016, Brazil is expected to be the fifth largest economy in the world and it desperately wants the Games to be a coming-of-age party for the emerging nation.

Although city officials have seized on the Games as an opportunity to attack long-term urban problems, there has been criticism of the billions of dollars that will be spent readying for the sporting events. The Olympics and Paralympics are expected to require a $14.4 billion budget, including $11.6 billion in public investments.

Rio Mayor Eduardo Paes says the city wants legacy projects that will continue to benefit the city long after the soccer balls and swimming goggles have been packed up.

“We know we can’t turn this Olympiad into a tear-down here and a white elephant there,’’ Paes said at a London news conference.

Among the projects that Rio hopes to have ready for the Olympics:

•  Transportation — Some 124 miles of public transportation lines are expected to be built over the next six years. Four Bus Rapid Transit corridors that would connect the four main Olympic venues, the airport and a new Ipanema subway link running to Barra da Tijuca, site of the Olympic village, are expected to be done by 2016. The Transoeste BRT, which began operating in June, has already won high marks from workers for reducing long commute times.

A light rail system also is slated to be built. It will connect the new port zone, Santos Dumont Airport — a domestic airport near Rio’s famed Sugarloaf Mountain, and a new tourist hub that is being developed in the city center.