How to find wind speed.

Question

An executive flew in the corporate jet to a meeting in a city 1500 miles away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 miles to go. If the air speed of the plane was 600 miles per hour, how fast was the wind blowing??

(ASSUME THAT THE WIND DIRECTION WAS PARALLEL TO THE FLIGHT PATH AND CONSTANT ALL DAY)

Answer 1

Let

Vp = plane speed = 600 mph (given)

Vw = wind speed

Equation 1:

Vp + Vw = 1500/T

600 + Vw = 1500/T

Solving for T,

T = 1500/(600 + Vw)

where

T = time it took plane to travel 1500 m

Equation 2:

Vp - Vw = 1200/T

600 - Vw = 1200/T

Solving for T,

T = 1200/(600 - Vw)

Equating the two values for "T",

1500/(600 + Vw) = 1200/(600 - Vw)

and cross multiplying

(600 - Vw)1500 = 1200(600 + Vw)

900,000 - 1500Vw = 720,000 + 1200Vw

Combining terms to solve for Vw,

1500Vw + 1200Vw = 900,000- 720,000

2700Vw = 180,000

Vw = 67 mph

Answer 2

Well let me give this a shot lol. Well David N is right though. The answer I got is assuming that it is relative to the first flight and it is parallel to the flight path.  

So the first thing I did was how long it took for the first flight path with D=RT.

So 1500=600(X)

X=15/6 or 2.5 hours.

So it took 2.5 hours for the first flight.  And you said that traveling the same amount of time the pilot said they still had 300 miles left to go.

So that means they traveled 1200 miles in the same amount of time. But we do not know there actual speed with the wind blowing against them. So I did an other D=RT.

1200=(X) (2.5)

X=480 miles an hour.

Now we know there speed with the wind blowing against them. Sense the air speed of the plane is 600 I just subtracted. So 600-480= 120 miles an hour for the wind speed.

I have no idea if this is right XD but hey I gave it a shot. Looks good to me though.