You and your friend are running at a long racetrack. You pass the starting line while running at a constant \(4.0 \mathrm{~m} / \mathrm{s}\). Fifteen seconds later, your friend passes the starting line while running at \(6.0 \mathrm{~m} / \mathrm{s}\) in the same direction, and at the same instant you increase your speed to \(5.0 \mathrm{~m} / \mathrm{s}\).

(a) How long does it take for your friend to catch up with you?

(b) How far are the two of you from the starting line when your friend catches up with you?