Your distance from Seattle after two hours of driving at 62 mph, from a starting point 38 miles east of Seattle, will be (38 + [62 mph][2 hr] ) miles, or 162 miles (east).
Your friend will be (20 + [65 mph][2 hrs] ) miles, or 150 miles south of Seattle.
Comparing 162 miles and 150 miles, we see that you will be further from Seattle than your friend after 2 hours.
After how many hours will you and your friend be the same distance from Seattle? Equate 20 + [65 mph]t to 38 + [62 mph]t and solve the resulting equation for time, t:
20 + [65 mph]t = 38 + [62 mph]t
Subtract [62 mph]t from both sides of this equation, obtaining:
20 + [3 mph]t = 38. Then [3 mph]t = 18, and t = 6 hours.
You and your friend will be the same distance from Seattle (but in different directions) after 6 hours.