Systems of equations word promblems. i need answering this questions > . < tysm. explain it also. 3)flying to kampala with a tailwind a plane averaged 158 km/h. on the return trip the plane only averaged 112 km/h while flying back into the same wind. find the speed of the wind and the speed of the plane in still air

Answers:
Speed of Wind = 23 km/hr
Speed of Plane in Still Air = 135 km/hr




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



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



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

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



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

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