This printable worksheet may be useful: Unequal Averages.
This problem featured in an NRICH webinar in December 2020.
You may wish to look at Wipeout as a follow-up activity.
The Inquiry Maths website offers a related activity and explains how it can be used as an inquiry prompt in the classroom.
Here is a photo of some of the contributions offered by delegates at the ATM Conference in 2015.