Down the road, floodwaters ate away everything but a precarious sliver of the right lane, which teeters at the edge of a newly carved precipice like a donkey path on the rim of a canyon. A collapsed bridge in the nearby town of Jamaica looks like a beaver dam, buried under the fallen trees and branches that flowed down the Ball Mountain Brook and knocked the bridge down.

Of all the challenges facing Vermont as it tries to recover from the floods caused by the remnants of Hurricane Irene, there may be none more daunting — or vital to solve — than repairing and reopening the hundreds of roads and dozens of bridges that the storm knocked out. In many spots, the roads must be fixed before equipment can be brought in to repair everything from homes and businesses to the power grid, railroad tracks and water and wastewater systems.

It is a race against time: winter comes early here, and there are just two and a half months before snowfall and frozen ground typically halt the state’s short road-building season.

“I think for a lot of us this is going to be the challenge of a lifetime,” said Joseph Flynn, an official at the Vermont Agency of Transportation who is in charge of one of the new quasi-military incident-command centers that the state set up to coordinate the mammoth task. Several hundred National Guard troops have added muscle, running huge olive drab bulldozers and backhoes alongside the yellow equipment of state workers and contractors.

The topography in this mountainous state — where, for centuries, the easiest way to run roads through the mountains has been to locate them along the edges of the rivers and brooks that had already found a path through — left many roads vulnerable to flooding, and tough to fix.

“We have areas where we have a mile or more of road that has disappeared into the water,” Mr. Flynn said. “And the upside of the road is all hill. So now you come from a forested hill to bare earth to the rivers. This is thousands of yards long, where you go from the hillside to where the road used to be right to the river.”

The repair work can be dangerous: two contractors shoring up a bridge in Clarendon found themselves cut off by a flash flood on Thursday, and had to be rescued by helicopter.

In some places, stranded residents have taken matters into their own hands. When a bridge was shut down in Royalton, isolating many residents, local fire and rescue workers cleared a path through a sunflower field at the Hidden Meadow Farm. Uprooting a tree that stood in the way, they cut a hole in a chain-link fence to allow residents to temporarily drive their cars right onto Interstate 89 on what may be the shortest on-ramp in the country.

“They’re calling it the Hillbilly Highway,” said Rachel Bigelow, who set up a little farm stand selling sunflowers, tomatoes and corn by the jury-rigged interstate entrance that now cuts through her farm. Evelyn Saenz, a Royalton resident who drove through it on Thursday, praised it as “Vermont ingenuity” and had another name for it: “Exit 2 1/2.”

Faced with so much devastation, state officials are taking a triage approach. The first order of business was restoring access to 13 towns that were isolated when the roads and bridges were washed out. They did this by building what state officials call “goat paths,” pouring gravel and sand and storm debris onto washed-out roads, and flattening them until they were strong enough for emergency vehicles to get over them.

Wardsboro was the last town to be reconnected, when the final link was finished Wednesday.

“I’ve been trapped for days,” said Norman Bills, 42, a rural mail carrier, as he stood at the ruins of his home on Wardsboro Brook. “We could go a half a mile that way and a half a mile this way. Now, hopefully tomorrow, I can get out of here and go back and try to do some work.”

Just this summer, Mr. Bills said, the brook was such a weak trickle that his children could hardly find a place in it to swim. But on Sunday it burst its banks and tore off the garage and dining room of his family’s home, which once belonged to his great-grandfather, washing away a venerable apple tree and sending his wood-burning stove downstream into a neighbor’s lawn.

“I don’t picture that there’s any coming back here, unfortunately, as beautiful a spot as it was and as enjoyable as it was to be on the river,” he said. “It’s done. But we’re all safe, and that’s all I care about.”

Now state officials are turning to other priorities: strengthening roads so they can handle repair trucks and easing the “you can’t get there from here” woes that the state charted on a Google map of road closings, especially the blocked east-west routes in southern Vermont. Trucks need to be able to restock the stores and gas stations that residents rely on. And with the state’s biggest tourism seasons approaching — fall foliage and winter skiing — there is plenty of work to do to get the roads ready for the tourists “from away.”

Brian Searles, the state’s transportation secretary, said that nearly half the closed state roads had already been reopened at least partly. “We will not be overwhelmed by this,” he said. “We will conquer the obstacles that exist.”

At the command center in Dummerston, Mr. Flynn tried to bolster his troops at a morning staff meeting by quoting a speech Calvin Coolidge gave when he returned to his native Vermont as president to help the state recover from the floods of 1927.

“I love Vermont because of her hills and valleys, her scenery and invigorating climate,” Mr. Coolidge said then, “but most of all because of her indomitable people.”

Mr. Flynn said later while holding a printout of an e-mail of the speech: “This may be corny, but it is something that was sent to me last night. It’s always been my favorite quote of Calvin Coolidge, but I never knew it was attributed to the flood of 1927. I think it says it all right there.”