84 minutes
1) Since we are dealing with the average then we need to plug all those 4 durations on this formula:
[tex]\begin{gathered} \bar{x}=\frac{71+74+78+78+t}{5} \\ 77=\frac{71+74+78+78+t}{5}(\times5) \\ 385=71+74+78+78+t \\ 385=301+t \\ 385-301=t \\ t=84 \end{gathered}[/tex]Note that in the question there were two trips whose duration was 78 minutes.
2) Hene, the 5th trip was 84 minutes long