On this wall clock, the minute hand (black) and the sweep second hand (red) are the same length, while the hour hand (grey) is shorter. At the moment of time shown, the tips of the three hands form a triangle.
Question: If the clock starts at noon, then at what time after that do the tips of the three hands first become collinear?
An approximate answer in the form of a sketch is fine. If you wish to approach the problem quantitatively, then let's agree that the hour hand is three-fourths as long as the other two hands.