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# Pre Calc

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+175

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

Dec 9, 2019

#1
+1

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

Dec 9, 2019
#2
+106539
+1

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)

Dec 9, 2019
edited by CPhill  Dec 9, 2019