Question

Flying against the wind, an airplane travels 3920 kilometers in 4 hours. Flying with the wind, the same plane travels 12,780 kilometers in 9 hours. What is thethe rate of the wind?

Answer 1

`\begin{gathered} \text{flying against the wind: Distance = 3920km, Time = 4h} \\ \text{ rate(r) = }(D)/(T)\text{ = }(3920)/(4)\text{ = 980} \\ \text{flying with the wind: } \\ \text{ Distance = 12,780}km,\text{ Time = 9h} \\ \text{ rate(r) = }\frac{12,\text{ 780}}{9}\text{ = 1420} \\ r\text{ = rate of plane in still Air} \\ w\text{ = rate of wind.} \\ \text{Therefore:} \\ case1\colon(flying\text{ against wind) : r - w = 980}--------(1) \\ case2\colon(flying\text{ with wind) : r + w = }1420-------(2) \\ \text{solving equation 1 and 2 simultaneously, } \\ \text{ by elimination method, by adding equation (1) and (2)} \\ \text{ r + r = 980 + 1}420 \\ \text{ 2r = 2400} \\ \text{ r = }(2400)/(2)\text{ = 1200}(km)/(h) \\ \text{substituting r into equation (1)} \\ \text{ 1200 - w = 980} \\ \text{ -w = 980 - 1200} \\ \text{ -w = -220} \\ \text{ w = 220}(km)/(h) \end{gathered}`