Question

Baba Yaga lost her broom somewhere between her hut and Bald Mountain, and wants to get it back. She calculates that with a tailwind of 2 km/h, she can fly from her hut to Bald Mountain in 6 hours. Baba Yaga starts her trip, finds her broom 40 km before Bald Mountain, and turns around and flies home. The entire journey takes 9 hours. Find the speed Baba Yaga flies in quiet weather (with no tailwind or headwind).

Answer 1

The speed with which Baba Yaga flies in quiet weather (with no tailwind or headwind) is approximately 2.9 km/h

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