A small plane flying with the wind flew 360 miles in three hours flying against that headwind the plane took four hours to fly the same distance find the rate of the plane and the calm air in the rate of the wind

p = plane's speed in calm air

w = wind's speed

p + w = speed across the ground of the plane flying with the wind

p - w = speed across the ground of the plane flying against the wind

d = rt is the standard distance equation, where d=distance, r=rate, t=time

d = 800 miles is given

800 = 4(p+w) :: given that it takes 4 hrs with the wind to travel 800 miles

800 = 5(p-w) :: given that it takes 5 hrs against the wind to travel 800 miles

so we have

4(p+w) = 800

5(p-w) = 800

4p + 4w = 800

5p - 5w = 800

multiply the first equation by 5 and the second by 4

20p + 20w = 4000

20p - 20w = 3200

add them

40p = 7200

p = 180

substituting for p = 180, we can find w

4p + 4w = 800

divide by 4

p + w = 200

180 + w = 200

So,

w = 20

checking our work.

4(180+20) = 800??

4(200) = 800

Yes

5(180-20) = 800??

5(160) = 800

Yes.

The Plane flies at 180 mph in calm air.

The Wind is blowing at 20 mph.

Hope This Helps! Merry Xmas:)