So first we want to see how far ahead Richie gets after 30 minutes.
Since he rides at 6 mph, in 30 minutes, or 1/2 of an hour, he would've traveled 3 miles.
So now we want to see how much faster Vanessa rides then Richie.
12 mph - 6 mph = 6 mph
So she would gain 6 miles over him in 1 hour.
Since she's already 3 miles behind him, and we want to be 6 miles ahead of Richie, she would have to gain 9 miles on him.
So therefore, since 9/6 = 1.5, and we want to know Richie's time, so + 0.5 which equals 2, we know that Richie has been riding for 2 hours.