Hi there! Thank you for the opportunity to help you with your question!

We can model the man's position by his speed multiplied by time. That is x = 1.2*t.

Now the dog's position has a delay, since it starts later. x_dog = 3.9*(t - 1.8) (we shift the time coordinate to account for the delay, so that at t = 1.8, the dog is at position zero).

In order to calculate how far they will have traveled when the dog catches up, we first need to find at what time they will meet. This is done by setting the two equations equal to one another:

1.2*t = 3.9*(t -1.8)

Solving for t gives:

t = 2.6 seconds.

In order to calculate the distance they've travelled, we can plug in t = 2.6 into either equation, and we'll get

x = 1.2 * 2.6 = 3.12 meters

Please let me know if you need any clarification. Always glad to help!