Rate of the plane in calm air is 162.6 miles per hour and the rate of the wind is 7.5 miles per hour
Solution:
Given that Â
Flying with the wind, a small plane flew 340 mi in 2 hrs .
Flying against the wind, the plane could fly only 310 mi in 2hrs Â
Need to find the rate of the plane in calm air and the rate of the wind.
As Flying with the wind, a small plane flew 340 mi in 2 hrs , Â
So speed(rate) of the plane when  Flying with the wind = [tex]\frac{340}{2} = 170[/tex] miles per hour
As flying against the wind, the plane could fly only 310 mi in 2hrs ,
So speed (rate) of the plane when  Flying against the wind = [tex]\frac{310}{2}=155[/tex]miles per hour
Let assume speed(rate) of the pane in calm air = x miles per hour Â
And speed(rate) of the wind = y miles
As  speed ( rate ) while Flying with the wind = speed(rate) of the pane in calm air + speed(rate) of the wind
=> 170 = x + y
=> x + y = 170 Â ------(1)
As  speed ( rate ) while Flying against the wind = speed(rate) of the pane in calm air - speed(rate) of the wind
=> 155 = x – y
=> x – y = 155  ------(2)
Adding (1) and (2) , we get
(x + y) + ( x - y) Â = 170 + 155
=> 2x = 325
=> [tex]x = \frac{325}{2}=162.5[/tex]
Substituting value of x in equation 1 , we get
162.5 + y = 170
=> y = 170 – 162.5 = 7.5 Â
Hence rate of the plane in calm air = x = 162.6 miles per hour and the rate of the wind = y = 7.5 miles per hour.
