Question 308701
You will need to use the formula d=vt, where d=distance, v=velocity (or speed) and t=time.


Write down what you know. Note that I will use i to denote Initial trip, and r to denote Return trip.


di=2400 miles
ti= 4 hours
vi=Vp+Vw

Where Vp=speed of plane in calm air and Vw=speed of wind. I am adding it because the plane is moving with the help of the wind behind it.


On the return trip,


dr=2000 miles
tr = 4 hours
vr = Vp-Vw


This time I subtract the wind's speed, because it is pushing against the plane in the opposite direction.


First equation:

di=vi*ti
2400=(Vp+vw)(4)
600=Vp+Vw
Vp=600-Vw


Second equation:

dr=vr*tr
2000=(Vp-Vw)(4)
500=Vp-Vw


Use substitution from Equation 1 into Equation 2 to solve for Vw:

500=(600-Vw) - Vw
-100=-2Vw
Vw=50mph


Which means that the plane's speed in calm wind is 550mph, because Vp+Vw=600, so Vp=550 mph.