Answer:
The speed of airplane is 207 miles per hour
The speed of wind is 23 miles per hour
Step-by-step explanation:
Given as :
The distance cover by airplane against the wind = D = 460 miles
The time taken to cover D distance = T = 2.5 hours
Again
The distance cover by airplane with the wind = d = 460 miles
The time taken to cover d distance = t = 2 hours
Let The speed of airplane = x mile per hour
Let The speed of wind = y miles per hour
According to question
∵ Speed = [tex]\dfrac{\textrm Distance}{\textrm Time}[/tex]
For Against the wind
x - y = [tex]\dfrac{\textrm D}{\textrm T}[/tex]
Or, x - y = [tex]\dfrac{\textrm 460 miles}{\textrm 2.5 hours}[/tex]
Or, x - y = 184 mph ........1
For with the wind
x + y = [tex]\dfrac{\textrm d}{\textrm t}[/tex]
Or, x + y = [tex]\dfrac{\textrm 460 miles}{\textrm 2 hours}[/tex]
Or, x + y = 230 mph ........2
Now, Solving eq 1 and eq 2
(x - y) + (x + y) = 184 mph + 230 mph
Or, (x + x) + ( - y + y) = 414 mph
Or, 2 x + 0 = 414 mph
∴ x = [tex]\dfrac{414}{2}[/tex]
i,e x = 207 mph
So, The speed of airplane = x = 207 miles per hour
Now, Put the value of x into eq 1
∵ x - y = 184 mph
So, 207 mph - y = 184 mph
Or, y = 207 mph - 184 mph
i.e y = 23 mph
So, The speed of wind = y = 23 miles per hour
Hence, The speed of airplane is 207 miles per hour and The speed of wind is 23 miles per hour . Answer
