Ok, first some theory:
I'm sure you know Newton's Second Law for linear motion:
F=maThis law can be extended for angular motion, ie
τ=Iα, where
τ is the magnitude of the torque (or moment),
I is the moment of inertia and
α is angular acceleration.
Furthermore, the moment of inertia
I of a point particle of mass
m spinning around a radius
r is
I=mr2, and a compound shape made up of many parts has a moment of inertia equal to the sum of the moments of inertia of all the little parts that make it up.
Now let's consider the question:
In the first case, the two children are both exerting a force
F on the roundabout tangentially, ie they are applying a couple (you should have met this topic at AS-level). How do the two forces they apply add in the couple to give a resultant moment, aka a resultant torque? Then use Newton's second law for angular motion.
In the second case, one child has jumped onto the roundabout. First, you need to find the moment of inertia of this new compound object, using the hints I've given above, and consider how the other child's single force gives a resultant moment/torque, and then apply Newton's second law again. We want both angular accelerations to be constant. You should be able to work it out from here.