Question 1177756
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).
let  the speed in still air be x
tailwind of 2 km/ h, 
Forward effective speed =( x+2) km/h
Time taken to reach bald mountain = 6 hours
Distance= speed * time = 6(x+2) km
But she finds the broom 40 km before
So that distance is 6(x+2)-40  
Actual distance with tailwind/speed
 ={{{ (6(x+2)-40)/(x+2)}}}

Return speed = (x-2) km/h
Return time = {{{(6(x+2)-40)/(x-2)}}}

{{{(6(x+2)-40)/(x+2) + (6(x+2)-40)/(x-2)=9}}}

{{{((6x+12-40)/(x+2))+((6x+12-40) /(x-2))=9}}}

{{{((6x-28)/(x+2))+( 6x-28)/(x-2)=9}}}

{{{(x-2)(6x-28) + (x+2)(6x-28)= 9(x^2-4)}}}

{{{6x^2 -28x -12x+56 + 6x^2-28x+12x-56 = 9x^2-36}}}

{{{12x^2-56x=9x^2-36}}}

{{{3x^2 -56x+36=0}}}

Solve for x

x=18 

18km/h in still water