Marcus du Sautoy presents a problem about his imagined commute to work. He can travel 10mph on the way there, and 15mph on the way back. The distance is fixed, so the question is, what is his average speed over the whole journey? Panellists on his puzzle game work towards the solution - which is not simply the mean of the two numbers. Du Sautoy presents the solution, using speed = distance / time.
Use as a challenge question or plenary related to study of distance, speed and time. Discuss with students the importance of considering the time taken in each part of the journey to work out the mean. Constructing equations or speed/ time graphs may help this.