1. **State the problem:** We need to find the average wind speed affecting a plane flying from Orlando to London and back, given the plane's airspeed and the times for each leg. 2. **Define variables:** Let $d$ be the distance between Orlando and London. Let $w$ be the wind speed (what we want to find). The plane's airspeed (speed in still air) is $550$ mph. 3. **Write equations for each leg:** - Flying from Orlando to London, the plane's ground speed is $550 + w$ mph. - Flying back, the ground speed is $550 - w$ mph. 4. **Use the time formula:** Time = Distance / Speed From Orlando to London: $$8 = \frac{d}{550 + w}$$ From London to Orlando: $$9.5 = \frac{d}{550 - w}$$ 5. **Express $d$ from both equations:** $$d = 8(550 + w)$$ $$d = 9.5(550 - w)$$ 6. **Set the two expressions for $d$ equal:** $$8(550 + w) = 9.5(550 - w)$$ 7. **Expand both sides:** $$4400 + 8w = 5225 - 9.5w$$ 8. **Combine like terms:** $$8w + 9.5w = 5225 - 4400$$ $$17.5w = 825$$ 9. **Solve for $w$:** $$w = \frac{825}{17.5}$$ 10. **Calculate $w$:** $$w = 47.142857...$$ 11. **Round to nearest mph:** $$w \approx 47$$ **Final answer:** The average wind speed is approximately 47 mph. This corresponds to Option A.