Ben(55 kg) is standing on very slippery ice when junior(25kg) bumps into him. junior was moving at a speed of 8m/s before the collision and ben and junior embrace after the collision. find the speed of ben and junior as they move across the ice after the collision .

Define
m₁= 55 kg, mass of Ben
m₂ = 25 kg, mass of Junior

v₁ = 0, initial speed of Ben (he was stationary)
v₂ = 8 m/s, speed of Junior

Consider the motion of Ben and Junior as occurring within a closed system.
Because momentum is preserved, the initial momentum of the system is equal to the final momentum of the system.

Refer to the figure shown below.
The initial momentum is
P₁ = m₁v₁ + m₂v₂
    = (55 kg)*(0 m/) + (25 kg)*(8 m/s)
    = 200 (kg-m)/s

Let V =   the speed of Ben and Junior (in an embrace) after the collision.
The final momentum is
P₂ = (m₁ + m₂)V
    = (55+25 kg)*(V m/s)
    = 80V (kg-m)/s

Equate P₁ and P₂ to obtain
80V = 200
    V = 2.5 m/s

 2.5 m/s