Question

Flying against the wind, an airplane travels 3920 kilometers in 8 hours. Flying with the wind, the same plane travels 5580 kilometers in 6 hours. What is the rateof the plane in still air and what is the rate of the wind?

Answer 1

Let the rate of the plane in still air be v;

Let the rate of the plane with the wind be u;

Thus, when the airplane flies against the wind, we have;

$\begin{gathered} d=3920\operatorname{km},t=8\text{hours} \\ v-u=\frac{3920}{8} \\ v-u=490\ldots\ldots\ldots\ldots\text{equation 1} \end{gathered}$

Also, when the same airplane flies with the wind, we have;

$\begin{gathered} d=5580\operatorname{km},t=6hours \\ v+u=\frac{5580}{6} \\ v+u=930\ldots\ldots\ldots\ldots\ldots\text{equation 2} \end{gathered}$

Thus, we solve equation 1 and equation 2 simultaneously by subtracting equation 1 from equation 2. We have;

$\begin{gathered} v-v+u-(-u)=930-490 \\ 2u=440 \\ u=220 \end{gathered}$

Thus, we substitute the value of u in equation 2, we have;

$\begin{gathered} v+u=930 \\ v+220=930 \\ v=930-220 \\ v=710 \end{gathered}$

Hence, the rate of the airplane in still air is 710km/hour and the rate of the airplane with the wind is 220km/hour.