Answer
1.33 s
Work Step by Step
We add the time for the radio signal to travel to Earth, and the time for the sound to travel in air to you. Use the relationship d = vt, twice. Solve for the times and add them together.
First consider the transit time for the EM wave. Use d = the Earth–Moon distance (from the inside front cover),
$d_{moon/Earth}=384\times10^{6}m $.
To be more accurate, subtract the Earth’s radius and Moon’s radius from this distance because the astronaut and the radio receiver are on the near sides of the moon and the Earth.
$d_{revised}=384\times10^{6}m-6.38\times10^{6}m -1.74\times10^{6}m $
$$t_{EM}=\frac{d}{v}=\frac{ d_{revised}}{3.00\times10^8m/s}$$
Finally, add the travel time from the loudspeaker to you.
$$t=t_{EM}+\frac{28m}{343m/s}=1.33 s$$
The microphone must have been inside the helmet. There is no air on the moon to convey sound waves.
