Dear Student,

the velocity of sound and wind are added vectorially.
therefore, in the first case,

v + u = x/t₁ ........................ (1)

v - u = x/t₂ ...........................(2)
on adding, we get
v = x (1/t₁ + 1/t₂) /  2
on subtracting,
u = x (1/t₁ - 1/t₂) /  2

in the second case,

the resultant velocity and u are at 90⁰ to each other
therefore,if u make a rt. triangle, 
                                   
v acts as hypotenuse and u as a leg and resultant vel. towards B makes the other leg. therefore,
Resultant vel. =   v² - u² 
time taken =     x      
                            v² - u² 

Best Of luck

Cracking IIT just got more exciting,It’s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and winexciting gifts by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple click here to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal

Askiitian Expert