Question

An elevator moving down passes its neighbor, an elevator moving up. Their speed relative to one another is 8 m/s. What is the velocity of each elevator relative to someone standing on the first floor? Assume that the elevators are traveling at the same speed, and that the upward direction is positive.

Answer 1

relative velocities are additive in magnitude when two objects go towards each other

put more simply, since both elevators move the same speed, the two speeds must add up to 8 m/s. if two equal speeds add up to 8 m/s, what is each speed?

from there, consider direction: one elevator is going up, so it'll have the positive version of the speed from before, and the other one going down will have the negative speed