Mathematics

# Flying against the wind a jet travels 7740 miles in 9 hours. Flying with the wind the same jet travels 4000 80 miles in 3 hours. What is the rate of the jet in still air and what is the rate of the wind?

$j\ \rightarrow\ the\ rate\ of\ the\ jet\ in\ still\ air \\w\ \rightarrow\ the\ rate\ of\ the\ wind\\\\j-w= \frac{\big{7740\ miles}}{\big{9\ hours}}\ \ \ \Rightarrow\ \ \ j-w=860\ \frac{miles}{ hour}\\\\ j+w= \frac{\big{4080\ miles}}{\big{3\ hours}}\ \ \ \Rightarrow\ \ \ j+w=1360\ \frac{miles}{ hour}\\----------\\\\2j=(860+1360)\ \frac{miles}{ hour}\ \ \ \Rightarrow\ \ \ 2j=2220\ \frac{miles}{ hour}\ \ \ \Rightarrow\ \ \ j=1110\ \frac{miles}{ hour}$
$j+w=1360\ \frac{miles}{ hour}\ \ \ \Rightarrow\ \ \ w=(1360}-1110)\ \frac{miles}{ hour}=250\ \frac{miles}{ hour}\\\\\\Ans.\ the\ rate\ of\ the\ jet\ in\ still\ air\ is\ 1110\ \frac{mi}{hr} \ \ \ \\\\.\ \ \ \ \ \ and\ \ \ the\ rate\ of\ wind\ is\ 250\ \frac{mi}{hr}$