A hiker starts out up a mountain at 10:00am from an altitude of 300 feet. By 2:00pm, they reach the summit at a height of 1200 feet and take in the sights. The hiker then starts back down the trail. At 2:45pm they take a short break at 1000 feet and realize they forget their binoculars at the summit. After going back for the binoculars they head back down, reaching the start of the trail at 5:30pm. How many times during the hike does the Intermediate Value Theorem guar- antee that the hiker was at an altitude of exactly 1125 feet? Give as much information as you can about when those times occurred.