Answer:
The speed with which Baba Yaga flies in quiet weather (with no tailwind or headwind) is approximately 2.9 km/h
Step-by-step explanation:
In the question, we have;
The speed of the tailwind = 2 km/h
The time it takes Baba Yaga to the Bald Mountain = 6 hours
The location where Baba Yaga finds her broom = 40 km before Bald Mountain
The duration of the entire journey = 9 hours
Let 'v' represent the speed with which Baba Yaga flies in quiet weather (with no tailwind or headwind), we get;
(v + 2) × t = (v - 2) × (t - 9)
v·t + 2·t = v·t - 9·v - 2·t + 18
2·t = 18 - 9·v - 2·t
4·t = 18 - 9·v
t = 4.5 - 2.25·v
(v + 2) × 6 = (v - 2) × (t - 9) + 40
6·v + 12 = (v - 2) × (4.5 - 2.25·v - 9) + 40
6·v + 12 = (v - 2) × (-2.25·v - 4.5) + 40
With a graphing calculator, we have;
6·v + 12 + 2.5·v² - 0.5·v - 9 - 40 = 0
5·v² + 11·v - 74 = 0
Using the quadratic formula
v = (-11 ± √(11² - 4·5×(-74)))/(2·5)
v ≈ 2.9, or v ≈ -5.1
Therefore;
The speed with which Baba Yaga flies in quiet weather (with no tailwind or headwind), v ≈ 2.9 km/h
