Answer
No additional force is necessary.
Work Step by Step
We can find the speed of the slower barge after it loses $1000~kg$ of coal:
$(m-1000~kg)v_f +(1000~kg)v_0 = mv_0$
$(m-1000~kg)v_f = (m-1000~kg)~v_0$
$v_f = v_0$
Note that the speed of the slower barge does not change.
Therefore, no additional force is necessary.
