It’s a lot like one of those math problems that gave you fits in sixth grade: A salesman leaves home in Denver and drives his electric car to a meeting in Boulder. At the same time, a physicist driving the same model electric car sets out from her loft in Los Angeles, heading to an appointment near Anaheim.

For both, the traffic is light, and the cars consume an identical amount of battery power while traveling the same number of miles. Being purely electric, they emit zero tailpipe pollutants during their trips.

The test question: Are their carbon footprints also equal?

The answer may be a surprise. According to a report that the Union of Concerned Scientists plans to release Monday, there would be a considerable difference in the amount of greenhouse gases — primarily carbon dioxide — that result from charging the cars’ battery packs. By trapping heat, greenhouse gases contribute to climate change.

The advocacy group’s report, titled "State of Charge: Electric Vehicles’ Global Warming Emissions and Fuel Cost Savings Across the United States," uses the electric power requirements of the Nissan Leaf as a basis for comparison. The Leaf, on sale in the United States for more than a year and the most widely available electric model from a major automaker, sets a logical baseline.

The California part of the story is upbeat: A hypothetical Los Angeles Leaf would be accountable for the release of an admirably low level of greenhouse gases into the atmosphere, about the same as a gasoline car getting 79 mpg. But the Denver car would cause as large a load of greenhouse gases to enter the atmosphere as some versions of the gasoline-powered Mazda 3, a compact sedan rated at 33 mpg in combined city and highway driving by the Environmental Protection Agency.

In simple terms, the effect of electric vehicles on the amount of greenhouse gases released into the environment can span a wide range, varying with the source of the electricity that charges them. California’s clean power makes the Leaf a hero; the coal-dependent utilities serving Denver diminish the car’s benefits as a global-warming fighter.

The UCS report, which takes into account the full cycle of energy production, often called a well-to-wheels analysis, demonstrates that in areas where the electric utility relies on natural gas, nuclear, hydroelectric or renewable sources to power its generators, the potential for electric cars to reduce the amount of carbon dioxide emissions is great. But where generators are powered by burning a high percentage of coal, electric cars may not be even as good as the latest gasoline models — and far short of the thriftiest hybrids.

With gasoline hovering around $4 a gallon and mass-production EVs like battery-powered versions of the Ford Focus and Honda Fit (as well as plug-in hybrids like the Chevrolet Volt, Toyota Prius PHV and Ford Fusion Energi models) either on sale now or coming soon, the report arrives at an ideal time. Its analysis can help shoppers make informed decisions.

It also fills a gap: Many of the existing studies on electric-car efficiency were completed before models like the Leaf came to market; others have expressed their results in science-lab terms like pounds of carbon dioxide emissions per year, not especially useful to consumers. Automakers have not always helped their customers understand the issues, either, typically painting electrics and hybrids with a green brush and an idealistic setting.

The attempt to forge a simple message has created mistaken impressions, too. During a discussion with business leaders and journalists at the French Consulate in New York early this month, the chief executive of Nissan and Renault, Carlos Ghosn, doubled down in declaring an environmental edge for electrics over the best gasoline models.

"Even if you could use electricity only from coal," Ghosn said, "you’re still better off using an electric car than using gasoline."

It is a position that Nissan says it has held since the Leaf program began, yet the studies that the company offers in support of its position show electrics outperforming only vehicles with fuel economy ratings from about 27 to 36 mpg.

Assembled over nine months in 2011, the UCS report provides clarification in several ways, examining charging costs under various conditions and offering comparisons among the Leaf, the Mitsubishi "i" electric and the Volt plug-in hybrid. Most revealing, perhaps, is the geographical breakdown of electricity generation.

In a worst-case situation, with electric power generated from a high proportion of coal — as it is in a wide swath of the country’s midsection — an electric car or a plug-in hybrid will generate slightly more full-cycle global-warming emissions, as the report calls the greenhouse gases, than the best gasoline-engine subcompact. In areas where the cleanest electricity is available — regions served by hydroelectric, natural gas or nuclear generating plants — greenhouse gas emissions may be less than half that of today’s best gasoline-engine vehicles.

Put another way, for 45 percent of the U.S. population, an EV will generate lower levels of greenhouse gases than a gasoline-engine vehicle capable of 50 mpg in combined city-highway driving. Cities in this group include the predictable — Seattle, for example — as well as the less obvious, like Buffalo or New Orleans.

About 37 percent of Americans live in regions where a Leaf’s greenhouse gas emissions would equate to a gasoline-powered vehicle rated at 41 to 50 mpg Some 18 percent of the population lives in regions with a comparatively dirty power supply, where the well-to-wheels carbon footprint of a Leaf would be the equivalent of a vehicle rated at 31 to 40 mpg, typical of models like the Chevrolet Cruze, Ford Focus and Hyundai Elantra.

Here’s another way to look at it: If one region were completely dependent on coal for power, its electric cars would be responsible for full-cycle global-warming emissions equivalent to a car capable of 30 mpg in mixed driving. In a region totally reliant on natural gas, an electric would be equivalent to a 50 mpg gasoline-engine car.

The report divides the United States into 26 regions. Each region comprises a single interconnected electricity grid, although several utility companies may operate within a region. Because the utilities sell power among themselves, the emission levels for one city or utility cannot be pinpointed for every hour of every day, but regional analysis provides an approximation of average emissions over time.

The report’s analysis is based on the EPA’s 2007 Emissions and Generation Resource Integrated Database, the most recent compilation of data available. For each region, the average amount of global-warming emissions generated to produce a kilowatt-hour of electricity was calculated, taking into account emissions resulting from the transportation of fuel to the power plant.

To convert those power plant emission levels to an mpg figure, calculations were based on the power draw of the Nissan Leaf: 0.34 kilowatt-hours per mile. The Volt, which draws 0.36 kilowatt-hours per mile, requires slightly more power.

The report makes it possible to compare electrics with conventional hybrids that rely solely on a gasoline engine to charge their battery. In the dirtiest regions of the country, the hybrid would generate lower levels of full-cycle emissions than the electric car, but a breakdown of the data shows that more than half of Americans live in regions where an electric car has lower well-to-wheels carbon emissions than today’s best full-hybrid vehicles, while 17 percent live in areas where they would be equal.

Of course, conventional gas-powered vehicles are getting cleaner as engineering advances improve fuel economy and reduce emissions. On the other hand, electrics and plug-ins will become cleaner without technology changes as coal-burning power plants are replaced with natural gas, nuclear, hydroelectric, wind or solar facilities.

Don Anair, a senior engineer in the UCS clean vehicles program, said utilities in the dirtiest electric-grid regions of the United States generate 2.5 to 3 times more global-warming emissions than those in the cleanest regions, so there is much room for progress. But he sees the industry trending in the right direction.

"A number of old coal-fired power plants are now being retired," he said. "Given emission standards recently introduced by the current administration, any new coal-fired plants would be far cleaner than their predecessors."

According to 2010 data from the U.S. Energy Information Administration, 45 percent of the country’s electricity is generated by burning coal, the dirtiest fuel. Natural gas, a much cleaner fuel, accounts for 24 percent of electricity production, a figure that is shifting rapidly with price swings. Nuclear plants generate 20 percent of the nation’s power, while wind, solar and geothermal sources provide 3 percent.

While the report puts hard numbers on the current situation, it also points out the need for fundamental changes.

"To prevent the worst consequences of global warming," the report concludes, "the automotive industry must deliver viable alternatives to the oil-fueled internal-combustion engine — i.e., vehicles boasting zero or near-zero emissions."

© 2012 The New York Times Company