Peck found work as a preceptress and teacher of languages and mathematics at Saginaw High School, where she remained until 1874.

When she wrote home to tell her family about her plans, they thought it was "perfect folly" for her to want attend college and graduate at the age of twenty-seven.

Peck worked as schoolteacher in Providence, Rhode Island, as well as Saginaw, Michigan; Cincinnati, Ohio; and Montclair, New Jersey.

[4] Her hiking attire included a hip-length tunic, tall climbing boots, and a pair of baggy-kneed knickerbockers trousers, and a felt hat she secured with a veil.

[9] Three years later, in 1900, she climbed Monte Cristallo in the Italian Dolomites, the Jungfrau in Switzerland's Bernese Alps, and the Fünffingerspitze in Austria.

[citation needed] Peck's accomplishment would have bested Fanny Bullock Workman's ascent of the Himalayan Pinnacle Peak, at 6,930 metres (22,740 ft) it was the world record for highest altitude climb; however, Workman challenged Peck's claim of the new world's highest altitude record during her Huascarán climb.

The engineers established that Peck's Huascarán calculations had been wrong; she had misjudged the altitude by about 600 metres (2,000 ft), calculating it as 7,300 metres (24,000 ft) due to broken altimeters, meaning that Peck had obtained the Americas record in the Western Hemisphere, while Workman remained the world record holder for highest altitude climb.

[11][14] Peck later wrote a book about her experiences called A Search for the Apex of America: High Mountain Climbing in Peru and Bolivia, including the Conquest of Huascaran, with Some Observations on the Country and People Below (1911).

[2][15] In 1929–30, Peck made a seven-month trip, "mostly by airplane," around South America in order to demonstrate the ease and safety of commercial flights for airline passenger.

After returning to the United States she published her fourth and final book: Flying Over South America: Twenty Thousand Miles by Air (1932).

[2][9] Peck, who never married, started a world tour in 1935 at the age of eighty-four, but became ill while climbing the Acropolis of Athens.

[17] Peck's remains were cremated and her ashes were buried in the North Burial Ground cemetery in Providence, Rhode Island.

[9] Her personal papers (1873–1935), including diaries, correspondence, and photographs are housed at the Brooklyn College Library Archives and Special Collections.