There is a robot that steps between integer positions in 3-dimensional space. Each step of the robot increments one co-ordinate and leaves the other two unchanged. How many paths can the robot follow going from the origin (0, 0, 0) to (5, 6, 7)?

David and alton are training for a race. they spend 35 minutes stretching and then go on a 5 mile practice run. david runs at a pace of 7 min/mile. alton runs at a pace of 8 min/mile. write an equation for each runner that shows the total length of their workout. then solve each equation showing your work