We know that Jack travels between cities M and P , which are 500 miles apart, at an average speed of 400 miles per hour while going and at an average speed of 500 miles per hour while coming back, so the time taken by Jack to go and come back is $\(\frac{500}{400}\)$ hours \& $\(\frac{500}{500}\)$ hours respectively.


So, the average speed of Jack for the round trip is $\(\frac{ Total Distance }{ Total Time }\)\(=\frac{500+500}{\frac{500}{400}+\frac{500}{500}}=\frac{2}{\frac{5+4}{2000}}=\frac{4000}{9}=444.44 \mathrm{mph}\)$

$($ Using - Distance $=$ Speed $\times$ Time $)$

A is the answer

Note: - When two same distances are travelled at different speeds say $S_1 \& S_2$, the average speed for the entire journey is harmonic mean of the speeds i.e. $\(\frac{2}{\frac{1}{S_1}+\frac{1}{S_2}}=\frac{2\left(\mathrm{~S}_1 \times \mathrm{S}_2\right)}{\mathrm{S}_1+\mathrm{S}_2}\)$