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

• 18 km/h

Explanation:

Let the speed of Baba Yaga is x

• The speed with tailwind: x + 2
• The speed with headwind: x - 2

The distance to Bald Mountain:

• 6(x + 2)

The distance she actually travelled is less by 40 km:

• 6x + 12 - 40 = 6x - 28

The time she spent:

• (6x - 28)/(x+2) + (6x - 28)/(x -2) = 9

Solve for x to find the speed:

• ((6x + 12) - 40)/(x + 2) + ((6x - 12) - 16)/(x - 2) = 9
• 6 - 40/(x + 2) + 6 - 16/(x - 2) = 9
• 40/(x + 2) + 16/(x - 2) = 3
• 40(x - 2) + 16(x + 2) = 3(x+2)(x - 2)
• 40x - 80 + 16x + 32 = 3x² - 12
• 3x² - 56x + 36 = 0

Solving the quadratic equation we get:

• x = 18 km/h
• (x = 2/3 discounted as not realistic)