SOLUTION: a jet plane flying with the wind flew 2400 miles in 4 hours. Against the wind, the plane flew only 2000 miles in the same amount of time. find the rate of the plane in calm air a

Question 308701: a jet plane flying with the wind flew 2400 miles in 4 hours. Against the wind, the plane flew only 2000 miles in the same amount of time. find the rate of the plane in calm air and the rate of the wind.
Answer by texttutoring(324) (Show Source): You can put this solution on YOUR website!
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.
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