# Modeling Equation.

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• April 7th 2011, 05:49 AM
Sajjad
Modeling Equation.
I just don't understand how to start building equations, where to start. Plz Read the question below
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An aircraft flies 1062 miles with the wind at its tail. In the same
amount of time, a similar aircraft flies against the wind 738 miles. If the air speed
of each plane is 200 miles per hour, what is the speed of the wind? (Hint: Time
equals the distance divided by the speed.)
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The wind is in favor of the first air craft i.e. its pushing it and that's why it is able to cover more distance unlike the other air craft. so i can say that if x is the wind speed then for the first aircraft it is directly proportional so 200x, means its boosting the plane speed and for the other plane its 200/x as it is opposing it.

After this i go blank, now what. so plz help.

Answer is 36miles/hours
• April 7th 2011, 06:09 AM
NOX Andrew
The speed at which an aircraft flies is the sum of the speed of the aircraft and the wind. For example, if the speed of the aircraft is 100 miles per hour and the speed of the wind is 50 miles per hour, then the speed at which the aircraft flies is 100 mph + 50 mph = 150 mph.

In your example, the first aircraft travels 1062 miles with the wind at its tail. Let $t$ be the time in which the first aircraft travels the 1062 miles. Then, the rate $r_1$ at which the first aircraft flies is

$r_1 = \dfrac{1062}{t}$

The rate $r_1$ at which the aircraft flies is the sum of the speed of the aircraft $v_a$ and the speed of the wind $v_w$. Therefore,

$v_a + v_w = \dfrac{1062}{t}$

The speed of the aircraft is given as 200 mph, so

$200 + v_w = \dfrac{1062}{t}$ (1)

Similarly, the rate $r_2$ at which the second aircraft flies is

$200 - v_w = \dfrac{738}{t}$ (2)

(Note the speed of the wind $v_w$ is subtracted from the speed of the second aircraft aircraft because the second aircraft flies against the wind.)

We have a system of equations (equations (1) and (2)), which can be solved for $v_w$ (the speed of the wind).
• April 7th 2011, 06:24 AM
Soroban
Hello, Sajjad!

Quote:

An aircraft flies 1062 miles with the wind at its tail.
In the same amount of time, a similar aircraft flies against the wind 738 miles.
If the air speed of each plane is 200 mph, what is the speed of the wind?

Let $\,w$ = speed of the wind (in mph).

The first plane flies 1062 miles at $200\!+\!w$ mph.

. . This takes $\dfrac{1062}{200\!+\!w}$ hours.

The other plane flies 738 miles at $200\!-\!w$ mph.

. . This takes $\dfrac{738}{200\!-\!w}$ hours.

The two times are equal: . $\dfrac{1062}{200 + w} \;=\;\dfrac{738}{200 - w}$

Solve for $\,w.$

• April 7th 2011, 07:04 AM
Sajjad
Thanks Soroban. Would u kindly guide me for how to start modeling, some guide or some suggestions etc. thanks.