Answer
The mass of block B is $0.20~kg$
Work Step by Step
Let $v_A$ be the speed of block A and let $v_B$ be the speed of block B. Since block B travels 3.0 meters in the same time it takes block A to travel 1.0 meter, then $v_B = 3~v_A$.
By conservation of momentum, block A's momentum is equal in magnitude to block B's momentum. We can find the mass of block B:
$m_B~v_B = m_A~v_A$
$m_B = \frac{m_A~v_A}{v_B}$
$m_B = \frac{m_A~v_A}{3~v_A}$
$m_B = \frac{m_A}{3}$
$m_B = \frac{0.60~kg}{3}$
$m_B = 0.20~kg$
The mass of block B is $0.20~kg$
