Answer
The shortest possible time to wait for a response is 520 seconds.
Work Step by Step
We can assume that electromagnetic waves are used for communication.
We can use the Earth-sun distance to find the minimum distance between Earth and Mars:
$d = (2.28\times 10^{11}~m)-(1.5\times 10^{11}~m)$
$d = 7.8\times 10^{10}~m$
We can find the time for EM waves to travel twice this distance:
$t = \frac{2d}{c}$
$t = \frac{(2)(7.8\times 10^{10}~m)}{3.0\times 10^8~m/s}$
$t = 520~s$
The shortest possible time to wait for a response is 520 seconds.
