We have a distance between John and Ramona that is d = 24 miles.
We can graph this situation as:
They will meet at the same point and at the same time.
If we call x the length travelled by John to the meeting point, Ramona would have travelled (24 - x) miles.
As the time is the same for both, we can express the time as the distance travelled divided by the speed of each one:
[tex]\begin{gathered} t=\frac{d_{john}}{v_{john}}=\frac{d_{ramona}}{v_{ramona}} \\ \frac{x}{20}=\frac{24-x}{16} \end{gathered}[/tex]We can now solve for x as:
[tex]\begin{gathered} \frac{x}{20}=\frac{24-x}{16} \\ 16x=20(24-x) \\ 4x=5(24-x) \\ 4x=120-5x \\ 4x+5x=120 \\ 9x=120 \\ x=\frac{120}{9} \\ x=\frac{40}{3} \end{gathered}[/tex]Then, they will meet 40/3 miles from the point where John starts.
As we want to calculate the time, we can use the distance x and the speed of John to calculate the time:
[tex]t=\frac{x}{v}=\frac{\frac{40}{3}}{20}=\frac{2}{3}\text{ hours}[/tex]We can convert this to minutes to have an exact value:
[tex]t=\frac{2}{3}\text{ hours}*\frac{60\text{ min}}{1\text{ hour}}=40\text{ min}[/tex]Answer: they will meet after 40 minutes.
