An airplane travels 460 miles from san diego to san francisco in 2.5 hours, going against the wind. the return trip is with the wind, and takes only 2 hours. find the rate of the airplane with no wind. find the rate of the wind.

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 =

For Against the wind

x - y =  

Or, x - y =  

Or, x - y = 184 mph        ........1

For with the wind

x + y =  

Or, x + y =  

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 =

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

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step-by-step explanation: