Hi Novak,

Let Kylie's speed be v. She travels at that constant speed for t_{1}, and so before Mile begins riding she is a distance d_{1} = vt_{1} from him.

Mile rides his bike at a constant speed 4v, which is 4 times that of Kylie. Let's say that it takes a time T for Mile to catch Kylie. During that time, Kylie continues to walk. So, in time T she is a distance vt_{1} + vT from the starting point. During this same time Mile has ridden 4vT. Given that at this time T Mile has caught Kylie, this means that they are at equal distances from their starting point. So, you can equate their distances:

4vT = vt_{1} + vT

Subtract vT from each side.

3vT = vt_{1}

We can cancel out v.

So, 3T = t_{1}

Or

T = t_{1}/3 = (30 min)/3 = 10 min

So, Mile can catch Kylie in 10 min. It is interesting that their speeds don't matter, but only their speed ratio matters.