This applet represents 4 runners (Anna, Bill, Chris, and David) running a relay around a track. Their goal is to complete the race in 8 minutes, which would give them an average speed of 8minutes/mile (or 7.5mph). You can control how long it takes each runner to run a lap by moving the points along the time (x) axis.
This applet is the first of 4 applets leading up to a challenge to the reader about average rates. The questions below start with allowing you to solidify your understanding of average rates and are intended to lead you to some unintuitive consequences in the CHALLENGE applet.
1. Suppose Anna, Bill, and Chris all run their lap in 2 minutes. How fast does David need to run to ensure they finish the race in 8 minutes or less?
2. Suppose Anna takes 3 minutes to run a lap, Bill takes 3 minutes to run a lap, and Chris takes 2 minutes to run a lap. How fast would David need to run in order to finish the race in less than 8 minutes? (Note: This would ensure that the team would have an 8 minute per mile average.)
3. Suppose the team has an average of 10 minute miles going into the last lap. How fast would David need to run for the team to complete the race in 10 minutes? 9 minutes? 8 minutes? 7 minutes? What is the fastest possible overall average speed for the team? How is this shown graphically? How would you calculate this algebraically? (Note: Usian Bolt is widely accepted to be the fastest man in the world. His record is 27.44 mph or a ~2.19 minute mile)
4. How much control does David have over the average speed -- What is the slowest average the team can have going into the final lap if they want to complete the race in 8 minutes? How is this shown graphically? How would you calculate this algebraically?