Answer
The time it takes for the transmitted signals to travel from the spacecraft to the Earth is about 35 minutes.
Work Step by Step
The signals are transmitted in the form of electromagnetic radiation, which travels in vacuum at speed of light $c\approx2.998\times10^8m/s$
We know that $1mi\approx1609.344m$
So, $c\approx1.863\times10^5mi/s$
Therefore, the time it takes for the transmitted signals to travel from the spacecraft to the Earth is $$t=\frac{3.91\times10^8mi}{1.863\times10^5mi/s}$$$$t\approx2.099\times10^3s\approx2099s\approx35minutes$$
