Genesee & Wyoming Inc. agreed on Monday to buy one of its main rivals, RailAmerica, for about $1.4 billion in cash, uniting two of the country’s biggest short-line rail operators.

Under the terms of the deal, Genesee & Wyoming will pay $27.50 a share, a nearly 11 percent premium to RailAmerica’s Friday closing price.

The combined company will run 111 railroads covering more than 15,120 miles of track. Genesee & Wyoming said that it expects the merger to bolster its earnings per share by more than 10 percent next year, assuming that the deal is approved by the federal Surface Transportation Board.

Private equity is playing a role in the transaction. RailAmerica’s biggest investor is the Fortress Investment Group, which acquired the company in 2007. And as part of Monday’s deal, the Carlyle Group will invest up to $800 million in Genesee & Wyoming to help finance the transaction. Bank of America Merrill Lynch is also providing $2.3 billion in debt financing.

Besides Bank of America, Genesee & Wyoming was also advised by the law firms Simpson Thacher & Bartlett, Steptoe & Johnson and Thorpe Reed & Armstrong. RailAmerica was advised by Deutsche Bank and the law firm Skadden, Arps, Slate, Meagher & Flom.