A flight across the US takes longer east to west than it does west to east because of the plane having a headwind flying westward and a tailwind flying eastward. Suppose you are flying from Philadelphia, PA to San Diego, CA. The distance between the cities is 3870 kilometers and the plane's speed in 725 km/r. What is the speed of the wind?

Let w represent the wind speed.

time = distance/speed

round trip time = time going west + time going east

11 h = (3870 km) / ((725 - w) km/h) + (3870 km) / ((725 + w) km/h)

11 * (725 - w) (725 + w) = 3870 * ((725 + w) + (725 - w))

11 * (725² - w²) = 3870*2*725

11*725²-3880*2*725 = 11*w²

170,375 = 11*w²

124.45 ≈ w

The speed of the wind is approximately 124 km/h.