Answers:
Speed of Wind = 23 km/hr
Speed of Plane in Still Air = 135 km/hr
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Explanation:
First let's go over two definitions
Headwind = wind that is flowing in the opposite direction of the plane's direction of movement; i.e., wind that is coming from the head direction. Headwinds slow the plane down
Tailwind = wind that is coming from the tail of the plane and moving in the same direction as the plane's destination. Tailwinds speed the plane up
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Let
w = speed of wind
p = speed of plane in still air
both speeds are in km/hr
With a tailwind, the plane will speed up so it will go from p to p+w. Therefore, the first equation is
p+w = 158
since the new speed (wind+plane's movement without wind) is 158 km/hr
Similarly, in a headwind, the speed reduces to 112 so
p-w = 112
because we take the plane's speed p and subtract off the wind speed w that slows down the overall speed
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The system of equations is
p+w = 158
p-w = 112
Add up the equations and notice how w cancels
p+w = 158
p-w = 112
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2p+0w = 270
Leading us to
2p = 270
2p/2 = 270/2
p = 135
The speed of the plane in still air is 135 km/hr
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Use p = 135 to find w
p+w = 158
135+w = 158
135+w-135 = 158-135
w = 23
The speed of the wind is 23 km/hr
