You are jogging eastward at an average speed of \(2.0 \mathrm{~m} / \mathrm{s}\). Once you are \(2.0 \mathrm{~km}\) from your home, you turn around and begin jogging westward, back to your house. At one point on your return trip, you look to the north and see a friend. You run northward at a greater speed of \(3.0 \mathrm{~m} / \mathrm{s}\) to catch your friend. After jogging next to each other for a time (at \(3.0 \mathrm{~m} / \mathrm{s}\) ), you turn around (southward) and return at \(3.0 \mathrm{~m} / \mathrm{s}\) to your original path, and resume jogging at \(2.0 \mathrm{~m} / \mathrm{s}\) westward. If you return home \(40 \mathrm{~min}\) after you left, how far north did you run while catching and running with your friend?