An airplane averaged 160 miles per hour with the wind and 112 miles per hour against the wind. Determine the speed of the plane and the speed of the wind. Is this possible to calculate with the info presented?

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- May 18th 2008, 07:22 AMscrattorpedoAirplane and Wind speed problem
An airplane averaged 160 miles per hour with the wind and 112 miles per hour against the wind. Determine the speed of the plane and the speed of the wind. Is this possible to calculate with the info presented?

- May 18th 2008, 07:48 AMearboth
Let $\displaystyle v_p$ denote the speed of the plane and $\displaystyle v_w$ the speed of the wind. Then you have:

$\displaystyle \left|\begin{array}{l}v_p+v_w=160 \\ v_p-v_w=112\end{array}\right.$

Solve this system of simultaneous equations. I've got $\displaystyle v_p = 136\ \frac{mi}{h}$ and $\displaystyle v_w = 24\ \frac{mi}{h}$