# Thread: Linear Equation Story Problem

1. ## Linear Equation Story Problem

Wind Speed An executive flew in the corporate jet to a meeting in a city 1500km away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300km to go. If the air speed of the plane was 600km/hr, how fast was the wind blowing? (Assume that the wind direction was parallel to the flight path and constant all day)

Can someone help me figure this out? I've tried looking at it from several different angles but can't seem to figure it out. My math book sucks at explaining things, especially story problems, so there's no help there. And I'm taking this class online so I can't get any teacher assistance.

2. Originally Posted by akileez
Wind Speed An executive flew in the corporate jet to a meeting in a city 1500km away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300km to go. If the air speed of the plane was 600km/hr, how fast was the wind blowing? (Assume that the wind direction was parallel to the flight path and constant all day)

Can someone help me figure this out? I've tried looking at it from several different angles but can't seem to figure it out. My math book sucks at explaining things, especially story problems, so there's no help there. And I'm taking this class online so I can't get any teacher assistance.

1. Let t denote the traveling time and v the speed of the wind.

2. According to the text of your problem you get a system of simultaneous equations:

$\left|\begin{array}{rcl}(600+v) \cdot t&=& 1500 \\ (600 - v) \cdot t &=& 1200 \end{array}\right.$

(Remark: If the plane has still 300 km to go it has covered a distance of 1500 - 300 = 1200 km)

3. Expand the brackets and solve the system for v and t.

For confirmation only: I've got a windspeed of $v = \frac{200}3\ \frac{km}h \approx 66.6\ \frac{km}h$

3. would you mind going into more detail about step 3 please? I'm having a hard time putting everything together. Thank you!

4. Originally Posted by akileez
would you mind going into more detail about step 3 please? I'm having a hard time putting everything together. Thank you!
$\left|\begin{array}{rcl}(600+v) \cdot t&=& 1500 \\ (600 - v) \cdot t &=& 1200 \end{array}\right.$ .......... [1]

$\left|\begin{array}{rcl}600t+vt&=& 1500 \\ 600t - vt &=& 1200 \end{array}\right.$ .......... [2]

Now subtract the two equations columnwise:

$2 v\cdot t = 300 ~\implies~vt = 150$ .......... [3]

Plug in this value into one of the equations of [2]:

$600t - 150 = 1200~\implies~t = \frac{1350}{600} = \frac94$

Plug in this value into [3] and solve for v.

5. Great! I understand now. Thank you so much