two objects, and where they meet

1. The problem statement, all variables and given/known data
A worker with a mass of Mw is pulling on a mass-less rope that is attached to a box with a mass of mb on a friction-less surface. The worker pulls with a constant force starting at rest. The Worker is at x = 0, and the box is at xb Find the position at which they meet in terms given.

2. Relevant equations

x = xi + vi * t + 1/2 a * t2
F = m * a

3. The attempt at a solution

Using newton’s laws I know that the force on each object is equal, so

Fw = Fb

xw f = xw i + vw i* t + 1/2 a * t2

thus for the worker’s side of the equation
xw f = 1/2 a * t2

and the box moves

xb f = xb i + vb i* t – 1/2 a * t2

thus

xb f = xb i – 1/2 a * t2

since they meet xb f is equal to xw f

thus

1/2 a * t2 = xb i – 1/2 a * t2

xb i = 1/2 aw * t2 + 1/2 ab * t2

2 xb i = (aw + ab) * t2

t = √( ( 2 * xb i) / aw + ab)

then taking what I have just solved for time, and plugging that back into the basic kinematic equation to find the distance I get jibberish. So I’m not sure where to go from here.

xmeet = xinitial + 1/2 aworker * ( ( 2 * xb i) / aw + ab)

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