Micah walks on a treadmill at 4 miles per hour. he has walked 2 miles when luke starts running at 6 miles per hour on the treadmill next to him. if their rates continue, will luke’s distance ever equal micah’s distance? explain.

Let time taken by Luke to cover the distance = x hours Speed of Luke = 6 miles per hour Therefore, Distance covered by Luke = 6x (1) Speed of Micah = 4 miles per hour Since Micah walked 2 miles before Luke started running, Luke started 1/2 an hour after Micah started. Therefore time taken by Micah to cover the distance = x+1/2 Distance covered by Micah = 4(x + 1/2) (2) Equating (1) and (2) 6x = 4(x+1/2) 6x = 4x +2 2x = 2 x= 1 Therefore Luke would take 1 hour to cover the distance covered by Micah.