Imagine the plight of the urban grandmother—yours, maybe, or mine. If she had a car, she surrendered the keys long ago. The grocery store and a bus stop are just down the block, but her knees are bothering her, so she can't walk that far. The doctor's office is a few miles away. So is the senior center.

Cities have something for her, through the Americans with Disabilities Act. If you're not older, or disabled, you've probably had little contact with it. It's called paratransit. It's like the bus or subway, but more personalized (home pickups!), more cumbersome (make reservations days in advance!), and much more expensive. The Brookings Institution estimates American agencies spent $5.2 billion on paratransit in 2013—12.2 percent of all money spent on transit that year. Meanwhile, cities face a silver-haired transportation crisis. The number of Americans ages 65 or older will jump to 15 to 20 percent of the population by 2030. How will they all get around?

All is not gloom and doom. A report from New York University's Rudin Center for Transportation outlines new approaches that could save cities more hundreds of millions of dollars annually. The best news? The solutions already exist. Cities just need to embrace them.

Nana's Uber?

One solution namedrops a familiar friend: ridesharing. Private mobility companies like Uber, Lyft, and Bridj already have started working with transit agencies to fill gaps in service.