Holiday Contest 2025 - Guts Round - Set 5 Problem 3

Joe walks in a constant speed of r meters per second along a 600m long airport hallway alternating between 100m long sections with conveyors and sections without conveyors, beginning with a section without conveyors. When walking on a conveyor, it boosts Joe’s speed by 1 m/s. If Joe runs and increases his own speed to r+1 meters per second, he saves 40 seconds. Find 60r.