A turboprop plane flying with the wind flew 400 mi in 4 h. Flying against the wind, the plane required 5 h to travel the same distance. Find the rate of the plane in calm air and the rate of the wind.

Rate of the plane in calm air is 90 miles/hr and rate of the wind of wind is 10 miles/hr

Step-by-step explanation:

Average speed of plane in with wind = 400 / 4 = 100 miles/hr

Average speed of plane against wind = 400/5 = 80 miles/hr

Consider the speed of plane in wind be x miles/hr and speed of plane against wind be y miles/hr

As such speed of plane in wind would be x + y miles/hr and speed of plane against wind would be x - y miles/hr. i. e

x+y = 100

x-y = 80

by solving these two equation, we get

2x=180

x = 90 miles/hr

y=100-90

y = 10 miles/hr

hence, Rate of the plane in calm air is 90 miles/hr and rate of the wind of wind is 10 miles/hr