Computing Wind Speed

Question

The average airspeed of a single-engine aircraft is 150 miles/hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed? I don't know if this helps but there is also a picture with airplanes flying from one place to another with the wind going one way. The distance between the 2 places says 600mi, and with the wind is says 3 hours against is 4 hours..

Answer 1

distance=rate*time

d=rt

d=(150+w)*2

d=(150-w)*3

distances are equal

(150+w)*2=(150-w)*3

300+2w=450-3w

2w+3w=450-300

5w=150

w=150/5

w=30 mph is the wind speed

Answer 2

We know that the distance is the same each way and the plane speed is 150 mph each way. Furthermore, the equation to calculate speed: speed = (distance/time), or v = d/t. Rearranging the equation: d = (v x t)

Let d1 = distance with the wind and let d2 = distance against the wind. Therefor, d1 = d2.

Let t1 = time with the wind and t2 = time against the wind.

Let v1 = total speed with the wind. Total speed is the sum of the plane speed and wind speed: v1 = (vp + vw).

Let v2 = total speed against the wind. Total speed is the difference between plane speed and wind speed: v2 = (vp - vw). Now,

d1 = d2                                   substituting d with (v x t) since d = (v x t)

(v1 x t1) = (v2 x t2)                 substituting for each variable v1, t1, v2, t2

(vp + vw)2 = (vp - vw)3           substituting vp with 150

(150 + vw)2 = (150 -vw)3         multiply each side out

300 + 2vw = 450 - 3vw             solve algebraically

5vw = 150                                solve for vw

vw = 30

The wind speed, vw, is 30 mph.