Let x be the time taken to return
The time of the plane to Los Angeles would be:
[tex]\begin{gathered} \frac{60}{40}=\frac{2}{3} \\ \text{Then, the time would be x+2/3} \end{gathered}[/tex]By equalizing the equations for the distance between the trajectories:
[tex]\text{distance}=\text{speed}\cdot\text{time}[/tex][tex]\begin{gathered} 600x=525(x+\frac{2}{3}) \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 600x=525x+350 \\ 600x\cdot525x=350 \\ 75x=350 \\ x=\frac{350}{75} \\ x=4.6667\text{ hours} \end{gathered}[/tex]The return trip is 4.66 hours long.
To determine how far apart are the cities, we need to calculate the distance with the formula already provided:
[tex]4.6667\cdot600=2800\text{ mi}[/tex]The cities are 2800 miles apart.
