+318 A man flies a small airplane from Fargo to Bismarck, North Dakota—a distance of 180 mi. Because he is flying into a head wind, the trip takes him 2 h. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 h 15 min. What is his speed in still air, and how fast is the wind blowing?
speed in still air ____ mph
wind speed ____ mph
His speed to Bismarck =180 / 2 =90 mph
His speed going back =180 / 1.25 = 144 mph
His speed in still air =[90 + 144] / 2 =117 mph
Wind speed =[144 - 90] /2 = 27 mph
+129852 Distance / Rate = Time
Let spped of plane in still air = P
Let speed of wind = W
On the trip out the effective speed of the plane = (P - W) .....the wind is slowing the plane down
On the return trip the feective speed of the plane = (P + W)......the wind is speeding the plane up
On the trip out.....we have
180 / ( P - W) = 2
180 = 2(P - W)
180 / 2 = P - W
90 = P - W
90 + W = P (1)
On the trip back, (1hr 15 min = 1.25 hrs) we have that
180 / (P + W) = 1.25
180 / 1.25 = P + W
144 = P + W sub (1) into this for P
144 = (90+ W) + W subtract 90 from both sides
54 = 2W divide both sides by 2
27 = W = wind speed (in mph)
And using (1)....90 + W = P ....so.......90 + 27 = 117 = speed of plane in still air (in mph)
