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
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
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 ,
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
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 ------(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) = 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
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.
