At the local F1 race track, Eddie was testing the latest car.
During the eight test laps, he managed to average the first two laps at 100mph, the next two laps at 102mph, the next two laps at 140mph and the last two laps at 150mph.
What was his average speed for the entire 8 laps?
Set the track length to be a random number, e.g. 5 miles.
Therefore the first two laps took 10 miles ÷ 100 mph = 10 ÷ 100 hours. Similarly, the second two laps took 10 ÷ 102 hours, etc. The total time taken for 40 miles is therefore, 10/100 + 10/102 + 10/140 + 10/150 hours.
Therefore the average speed for the entire 8 laps is 40 ÷ (10÷100 + 10÷102 + 10÷140 + 10÷150) = 119 mph. QED.