Question

It takes a plane 40 minutes longer to fly from Boston to Los Angeles at 525 mi/hour that it does to return at 600 mi/hour. How long is the return trip and how far apart are the cities?

Answer 1

Let x be the time taken to return

The time of the plane to Los Angeles would be:

`\begin{gathered} (60)/(40)=(2)/(3) \\ \text{Then, the time would be x+2/3} \end{gathered}`

By equalizing the equations for the distance between the trajectories:

`\text{distance}=\text{speed}\cdot\text{time}`
`\begin{gathered} 600x=525(x+(2)/(3)) \\ \end{gathered}`

Solve for x:

`\begin{gathered} 600x=525x+350 \\ 600x\cdot525x=350 \\ 75x=350 \\ x=(350)/(75) \\ x=4.6667\text{ hours} \end{gathered}`

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:

`4.6667\cdot600=2800\text{ mi}`

The cities are 2800 miles apart.