Question

Jeff starts driving at 65 miles per hour from the same point that Lauren starts driving at 70 miles per hour. Theydrive in opposite directions, and Lauren has a half-hour head start. How long will they be able to talk on theircell phones that have a 340-mile range?

Answer 1

Since Lauren has a half-hour head start, let's calculate the distance covered in this time:

`\begin{gathered} distance=speed\cdot time\\ \\ distance=70\cdot0.5\\ \\ distance=35\text{ miles} \end{gathered}`

Since they are driving in opposite directions, the relative speed is the sum of speeds.

So, to find when the distance between then will be 340 miles, we can use the same formula, but now considering the initial position:

`\begin{gathered} final\text{ }position=initial\text{ }position+speed\cdot time\\ \\ 340=35+(65+70)\cdot t\\ \\ 135t=340-35\\ \\ 135t=305\\ \\ t=(305)/(135)\\ \\ t=2.26\text{ hours} \end{gathered}`

If we add the half-hour head start, the total time is 2.76 hours.