Question

If a palne can travel 480 miles per hour with the wind and 420 miles per hour against the wind, find the speed of the plane without a wind and speed of the wind. The speed of the plane in still air is ___miles per hour. The speed of the wind is ___ miles per hour.

Answer 1

In 1 hour, the plane flies 480 miles with the wind. Using the usual equation, \(d = v*t\), we can write our equations:
\(480 \text{ mi} = (v_{plane}+v_{wind})*1 \text{ hr}\)
\(420 \text{ mi} =(v_{plane}-v_{wind})*1 \text{ hr}\)

Solve that system of equations and you'll have the velocity of the plane in still air, and the velocity of the wind. Be sure to check your answers in the original equation for validity.