Answer
$8.04 \ s$
Work Step by Step
We first find the speed of the small block when it hits the large one:
$v = \sqrt{2(9.81)(.25)}=2.21\ m/s$
We find the speed of each block following the collision:
$v_{1f}=\frac{m_1-m_2}{m_1+m_2}v_{1i}+\frac{2m_2}{m_1+m_2}v_{2i}$
$v_{1f}=\frac{.2-.8}{1}(2.21)=-1.32\ m/s$
Using conservation of momentum, we find:
$v_{2f}=.884\ m/s$
Thus, we see that it will take $\frac{1.4}{1.32}=1.06 \ s$ for the small block to return to the ramp. Then, to go up and down the incline, we find:
$0=1.32t+\frac{1}{2}sin30gt^2 \\ t=.54 \ s$
When it returns, it will be going 1.32 meters per second, and the other block will be $((1.06+.54)(.884))+1.4=2.81$ meters away. Thus, we find that the time will be:
$t=\frac{2.81}{.436}+1.6=8.04 \ s$
