After nine months of being homeless, all Yolanda Pharr can think about is how much she misses a stove. She’s been living in a Days Inn motel room off New York Avenue with her six boys – four boys to one double bed, she and two boys to another — because DC General is full. She longs for the ordinary grace of cooking dinner.

“I am so tired of eating microwave food,” she tells her caseworkers.

Pharr, 30, has come to see her caseworkers at the District’s Virginia Williams Family Resource Center one summer morning to tell them she is finally willing to try Rapid Rehousing, a new program the city is pushing that quickly puts homeless families into their own apartments and helps them pay the rent for four months to a year, while caseworkers intensively work to ready them to be self-sufficient.

Pharr has been working for two months as a bus driver and says she loves it.

Now, all she needs to do is find an apartment. She climbs into her green Chevy Tahoe, drives from the city building tucked away among cranes, road work and construction projects in the booming NoMa area of Northeast D.C., across the Anacostia river into the more affordable Southeast D.C., and begins the hunt.

What she really wanted was at least a three-bedroom apartment for the seven of them. But most places she’d looked charged at least $1,350 a month, a price she fears she can’t pay.

She pulls up to a brick apartment complex in Southeast off Benning Road advertising itself as affordable housing.

Her eyes light up at the brochure showing gleaming hardwood floors, refurbished kitchens and sparkling, brand new stoves. A three bedroom apartment goes for $1,135. The location is perfect, near her sons’ schools and family child care.

A woman behind the counter at the rental office asks how much she makes a year to see if she’ll meet the minimum income requirements.

“I work 80 hours a week,” she says confidently. “Twelve hours a day. Five days a week. Eleven dollars an hour.”

The woman rings up the numbers on an adding machine, rips off the tape and hands it to Pharr. $47,850. Well within the income guidelines for a three-bedroom apartment.

“Wow, I didn’t know my income was that much!” Pharr squeals excitedly.

As she waits to make an appointment to tour one of the apartments, she slowly realizes that working 12 hours a day, five days a week means she works 60 hours a week. That put her annual income at $34,320. Barely enough to qualify for a two-bedroom apartment.

Her smile fades.

In the past 10 years, as the District has prospered, with booming development drawing a new class of striving young professionals, the number of apartments renting for $750 a month with utilities has dropped in half, to 34,000, one local study found, while rentals costing $1,500 more than tripled.

The fair market rent of a two-bedroom apartment has soared to $1,412 a month. That, one study found, would require a minimum wage worker earning $8.25 an hour to work 132 hours a week, 52 weeks a year. Another study found that nowhere in America can a minimum wage worker pay 30 percent of his or her income — the federal definition of affordable — and cover the cost of a two-bedroom apartment.

Katayah Dixon is a housing specialist for Community of Hope, one of the city’s homeless services contractors. Finding any affordable housing is one of the biggest challenges with the Rapid Rehousing program, she said. Finding affordable housing for large, low-income and homeless families like Pharr’s is close to impossible.

Families are recertified every few months to make sure they’re working on their plans to become self sufficient, so Rapid Rehousing subsidies are only guaranteed for three to four months at a time. Most landlords want year-long leases, she said.

“I ask them to take a risk on our clients,” she said.

Dixon spends her days driving around the city, mostly in Northeast and Southeast, she said, talking to landlords, looking at rents and compiling a list of potential apartments she hands out to homeless families at DC General to entice them into trying Rapid Rehousing.

At the shelter, Andreisha Ross, has taken that list and crossed out almost every single address. “NO WAY,” she’s written across some. “HECK NO,” on others.

“I’ve looked,” she said. “These are in drug-infested neighborhoods. People are sitting outside in their cars, gambling, watching your every move. They’re just the worst of the worst of the worst areas. And even then, they say we have to meet minimum income requirements.”

Ross wondered why she couldn’t get a Rapid Rehousing apartment in Northwest.

Dixon sighed.

“If you’re not working, you can’t afford $2,000 for a one-bedroom apartment in DuPont Circle,” she said. “A lot of clients have expectations that their finances cannot meet.”

Back at the brick apartment complex off Benning Road, Pharr picks up the application for the newly refurbished apartments with gleaming floors and the sparkling stoves. She grimaces, then checks the box for the two-bedroom apartment.

On the next line, the application asks “Number of Children? Pharr hesitates for a moment. Then she writes: “three.”