Consider the relation,
[tex]\text{Time}=\frac{\text{ Distance}}{\text{ Speed}}[/tex]Let the distance between Trent and Austin is 'd' kilometers.
Then the time taken by Trent to reach Austin is given by,
[tex]T_1=\frac{d}{45}[/tex]Similarly, the time taken by Trent on his return trip is given by,
[tex]T_2=\frac{d}{30}[/tex]Given that the trip to Austin was 1 hour less than the return trip,
[tex]\begin{gathered} T_2-T_1=1 \\ \frac{d}{30}-\frac{d}{45}=1 \\ d(\frac{1}{30}-\frac{1}{45})=1 \\ d(\frac{45-30}{30\times45})=1 \\ d=\frac{30\times45}{15} \\ d=2\times45 \\ d=90 \end{gathered}[/tex]Solve for the total time of the trip as,
[tex]\begin{gathered} T=T_1+T_2 \\ T=\frac{90}{45}+\frac{90}{30} \\ T=2+3 \\ T=5 \end{gathered}[/tex]Thus, the total time required for complete trip is 5 hours.
