Answer
(a) If they are running in the same direction then $v_2=3.5m/s$
(b) If they are running in the opposite direction then $v_2=8.17m/s$
Work Step by Step
There are two cases (a) They are running in the same direction (b) in the opposite direction
(a) The velocity of the lighter runner can be determined as follows:
Given that $P_1+P_2=350$
$\implies P_2=350-P_1$
$P_2=350-m_1v_1$
$\implies P_2=350-70(2)=210Kg.m/s$
$\implies m_2v_2=210$
$\implies v_2=\frac{210}{60}$
$\implies v_2=3.5m/s$
(b) If they are running in the opposite direction then
$P_2-P_1=350Kg.m/s$
$P_2=P_1+350=140+350=490$
$\implies m_2v_2=490$
$\implies v_2=\frac{490}{m_2}$
We plug in the known values to obtain:
$v_2=\frac{490}{60}$
$\implies v_2=8.17m/s$
