Answer
The new time will be 13 percent of the old, cutting the time by a factor of 7.7.
Work Step by Step
Use Poiseuille’s equation, 10-9, to find the reduced time. We see that the volume flow rate is proportional to $R^4$, all else being equal.
$\frac{Q}{R^4}=\frac{V}{t}\frac{1}{R^4}$ is constant. Assuming that the total volume V to water the garden is the same, we see that $tR^4$ is constant.
$$t_1R_1^4=t_2R_2^4$$
$$t_2=t_1(\frac{R_1}{R_2})^4= t_1(\frac{3/8}{5/8})^4=0.13t_1$$
The new time will be 13 percent of the old, cutting the time by a factor of 7.7.