# Math Help - Airplane and Wind speed problem

1. ## Airplane 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?

2. Originally Posted by scrattorpedo
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?
Let $v_p$ denote the speed of the plane and $v_w$ the speed of the wind. Then you have:

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

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