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:
![\begin{gathered} t=(d_(john))/(v_(john))=(d_(ramona))/(v_(ramona)) \\ (x)/(20)=(24-x)/(16) \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/db1nyebqy9aukv1eghv9.png)
We can now solve for x as:
![\begin{gathered} (x)/(20)=(24-x)/(16) \\ 16x=20(24-x) \\ 4x=5(24-x) \\ 4x=120-5x \\ 4x+5x=120 \\ 9x=120 \\ x=(120)/(9) \\ x=(40)/(3) \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/j7azvh88eg2xr1dxdex1.png)
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:
![t=(x)/(v)=((40)/(3))/(20)=(2)/(3)\text{ hours}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/bz0z177u8m29dhmld6rp.png)
We can convert this to minutes to have an exact value:
![t=(2)/(3)\text{ hours}*\frac{60\text{ min}}{1\text{ hour}}=40\text{ min}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/ej2ggdhiggygbdlvg1g0.png)
Answer: they will meet after 40 minutes.