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Question from Sandy, a student:

HARD!! algebra (Linear Systems) question?
An Airplane cruises at 120km/h in still air. One day, when the wind was blowing steady from the west, the airplane travelled west (flying into the wind) and landed at its desination after 1.5h. The airplane's return trip (flying with the wind) was only 1.0 h long. On both legs, the airplane travelled at its cruising speed. (meausred with respect to the air surrounding the airplane).

Part A
Write a System of equations that would allow you to determine the speed of the wind blowing that day and the distance travelled each way

Part B
When solving the system of equations graphically, what equations would you enter into the equation editior (to make graphs on your calculator)

Part C
Indicate what the X and the Y represent

Well.... I'm stumped...

y= 1.5(120-x) = 180 - 1.5x ??? now what do I do?
y= 1.0(120+x) = 120 + 1.0???
I'm so confused :( Please help me

Hi Sandy.

Distance divided by speed equals time. Let's use that to set up the equations:

Let D represent the distance between the origin and the destination.
Let W represent the windspeed.

Into the wind: D / (120 - W) = 1.5
Against the wind: D / (120 + W) = 1.0

I used D and W, not X and Y, but you can substitute if you prefer.

Can you do part B now?

Hope this helps,
Stephen La Rocque

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