Answer
(a) The tension in the rope is $13.7N$
(b) The acceleration of the 10-kg block is $1.37m/s^2$
Work Step by Step
1) The heavier block $(m_1=10kg)$
We assume that this block moves to the right with acceleration $a_1$. The only force acting to move the block to the right is the tension in the rope $T$.
$$T=m_1a_1=10a_1\hspace{2cm}(1)$$
2) The lighter block $(m_2=3kg)$
This block will go downward under its own weight $m_2g$. However, the movement is opposed by tension force $T$ in each of the 2 ropes hanging the block, the total of which is $2T$.
Assume that this block moves with acceleration $a_2$, $$m_2g-2T=m_2a_2$$ $$29.4-2T=3a_2\hspace{2cm}(2)$$
As mentioned in the hint, for an distance $x$ the lighter block moves, the heavier block moves a distance of $2x$, meaning that $a_1=2a_2 (3)$
We now solve equations (1), (2) and (3), and get $a_2=0.68m/s^2$, $a_1=1.37m/s^2$ and $T=13.7N$
