Answer
The final angular speed of the carousel is $1.83rad/s$
Work Step by Step
Before the person climbs aboard, the total moment of inertia is $$I_0=I_{carousel}=125kg.m^2$$
After the person climbs aboard, the person, with mass $m=40kg$, is $1.5m$ away from the axis of rotation, so the total moment of inertia is $$I=I_{carousel}+m(1.5m)^2=215kg.m^2$$
The carousel's initial velocity $\omega_0=3.14rad/s$. Angular momentum is conserved, so $$I_0\omega_0=I\omega$$ $$\omega=\frac{I_0\omega_0}{I}=1.83rad/s$$
