Let's assume the length of each lap of the track is the same.
To find the average speed for Jane to increase her average speed to 24 km/h, we need to consider the total distance traveled and the total time taken.
Since Jane has completed 4 laps at an average speed of 20 km/h, her total distance covered is 4 laps. Let's denote the length of one lap as "L."
Total distance covered = 4 laps * L
The total time taken to cover this distance can be calculated using the formula:
Total time = Total distance / Average speed
For the first scenario (average speed of 20 km/h):
Total time = (4 laps * L) / 20 km/h
For the second scenario (target average speed of 24 km/h):
Total time = (5 laps * L) / 24 km/h
Since the total time taken is the same in both scenarios (Jane completed 4 laps at an average speed of 20 km/h and then the fifth lap at a higher average speed), we can set up an equation:
(4 laps * L) / 20 km/h = (5 laps * L) / 24 km/h
Now, let's solve for the average speed required for the fifth lap.
Cross-multiplying the equation:
(4 laps * L) * 24 km/h = (5 laps * L) * 20 km/h
96 laps * km/h = 100 laps * km/h
Subtracting 96 laps * km/h from both sides:
4 laps * km/h = 100 laps * km/h - 96 laps * km/h
4 laps * km/h = 4 laps * km/h
Dividing both sides by 4 laps:
km/h = (100 laps * km/h - 96 laps * km/h) / 4 laps
Simplifying:
km/h = (4 laps * km/h) / 4 laps
km/h = km/h
Therefore, there is no specific average speed required for Jane to complete her fifth lap in order to increase her average speed to 24 km/h. As long as she maintains the same average speed for the fifth lap, her average speed will increase to 24 km/h.