Two particles, Particle A and Particle B, begin traveling away from a wall. Let t represent the number of seconds since the particles started moving, let a(t) represent Particle A's distance from the wall in feet t seconds after the particles started moving, and let b(t) represent Particle B’s distance from the wall in feet t seconds after the particles started moving.

a. Suppose f(t) represents the particles’ combined distance from the wall in feet t seconds after they started moving. Define the function f in terms of a and b.
f(t) =

b. Suppose g(t) represents how much further Particle B is from the wall than Particle A (in feet) t seconds after they started moving. Define the function g in terms of a and b.

g(t) =

c. t seconds after the particles started moving, Particle A’s distance from the wall is h(t) times as large as Particle B’s distance from the wall. Define the function h in terms of a and b.