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How long is 4,000 paces?

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It's about one-and-a-half times as long as The Kentucky Derby.
In other words, 4,000 paces is 1.515150 times the length of The Kentucky Derby, and the length of The Kentucky Derby is 0.6600010 times that amount.
(Churchill Downs, Louisville, Kentucky) (total race length)
The total race length of the Kentucky Derby run at Churchill Downs is 2,640 paces. First run in 1864, the Kentucky Derby is one of the oldest continuously-running sporting events in America, almost two years older than the Westminster Kennel Club Dog Show
It's about one-and-three-fifths times as long as The Preakness Stakes.
In other words, 4,000 paces is 1.5948960 times the length of The Preakness Stakes, and the length of The Preakness Stakes is 0.62700010 times that amount.
(Pimlico Race Course, Baltimore, Maryland) (total race length)
The total race length of the Preakness Stakes run at the Pimlico Race Course is 2,508 paces. Dubbed "the race for the Black-eyed Susans" after Maryland's state flower, the winning horse is actually draped with a garland of painted yellow daisies, as Black-eyed Susans do not bloom in time for the late-May race.
It's about three-fifths as tall as a Puncak Jaya.
In other words, 4,000 paces is 0.62410 times the height of a Puncak Jaya, and the height of a Puncak Jaya is 1.6020 times that amount.
(a.k.a. Mt. Carstensz, a.k.a. Carstensz Pyramid, a.k.a. Nemangkawi, a.k.a. Carstensz Toppen, a.k.a. Gunung Sukarno) (Papua province, Indonesia)
The highest point in Oceania (and therefore one of the seven summits) peak of Puncak Jaya is 6,409 paces. Dutch explorer Jan Carstenszoon, the mountain's namesake, is said to have been ridiculed for claiming to have seen snow near the equator when he reported his discovery of the peak in 1623.
It's about three-fifths as tall as a Vinson Massif.
In other words, 4,000 paces is 0.62310 times the height of a Vinson Massif, and the height of a Vinson Massif is 1.6050 times that amount.
(a.k.a. Mount Vinson) (Antarctica)
Mount Vinson, the highest peak of the Vinson Massif mountain, reaches 6,420 paces at its peak. The mountain is named after Georgia Congressman Carl Vinson who emphatically promoted Antarctic exploration in the 1930s.
It's about half as tall as Mount Elbrus.
In other words, 4,000 paces is 0.54020 times the height of Mount Elbrus, and the height of Mount Elbrus is 1.8510 times that amount.
(a.k.a. Mingi Tau, a.k.a. Эльбрус, a.k.a. იალბუზი) (Karachay-Cherkessia and Kabardino-Balkaria, Russia) (west summit)
The west summit of the dual-summit volcano Mount Elbrus is 7,404 paces at its peak and is the highest peak in both Russia and the European continent. Until 1976, a cable car would take visitors to the mountain as far up as the Garabashi camp, located at an elevation of 4,987 paces.
It's about half as tall as a Kilimanjaro.
In other words, 4,000 paces is 0.5174180 times the height of a Kilimanjaro, and the height of a Kilimanjaro is 1.932670 times that amount.
(a.k.a. Mount Kilimanjaro) (Tanzania) (to Uhuru peak; 2008 gravimeter measurement)
Kilimanjaro rises to 7,730.70 paces at its peak. An isolated peak with no surrounding mountain range, Kilimanjaro is considered the world's tallest freestanding mountain.
It's about half as tall as Mount Logan.
In other words, 4,000 paces is 0.51150 times the height of Mount Logan, and the height of Mount Logan is 1.9550 times that amount.
(Kluane National Park and Reserve, Yukon, Canada) (elevation)
The highest mountain in Canada, Mount Logan has a total height of 7,822 paces. The high altitude and northern latitude of the mountain resulted in one-time temperature of -77.5 °C — the lowest temperature ever recorded outside of Antarctica.