Answer:
Let's assume that the length of the athletics track is "L" units, and let "x" be the speed (in units per minute) at which you run the first lap.
Since you're running two laps, the total distance covered is 2L. The time it takes to complete the first lap is L/x, since time = distance ÷ speed. For the second lap, you want your average speed to be twice the speed of the first lap, so your total time for the second lap must be half the time of the first lap:
Total time for second lap = 0.5 * (L/x) = L/2x
The total time for the two laps is the sum of the time for each lap:
Total time = L/x + L/2x = (2L + L)/(2x) = 3L/(2x)
The average speed for the two laps is the total distance (2L) divided by the total time (3L/2x):
Average speed = (2L) / (3L/2x) = 4x/3
Since you want your average speed for the second lap to be twice the speed of the first lap, you can set up the following equation:
2x = (4x/3) - x
Solving for x, we get:
2x = 4x/3 - x
5x/3 = 0
x = 0
This means that you would have to run the first lap at a speed of 0 units per minute, which is impossible. Therefore, it's not possible to run two laps of an athletics track such that the average speed of the second lap is twice the speed of the first lap.
Explanation: