Answer
James' speed is 0.733 m/s.
Work Step by Step
The total momentum of the system is zero. Therefore, the magnitude of the momentum of each person will be equal.
$m_1v_1 = m_2v_2$
$v_1 = \frac{m_2v_2}{m_1}$
$v_1 = \frac{(60.0~kg)(1.10~m/s)}{90.0~kg}$
$v_1 = 0.733~m/s$
James' speed is 0.733 m/s.
