A plane travels speed at 225 mph in still air. Flying with tailwind, the plane is clocked over distance of 875 miles. Flying against headwind, it takes 1 hour longer to complete the return trip. What is the wind velocity?

Answer:The wind speed is 28.466 mi/hStep-by-step explanation:Let's call Vs=225mi/h the plane speed in still air. Let's have X=875 mi the distance traveledWe'll also call Vw the wind speed. In the first flight, the plane goes with a speed of Vs+Vw.The return trip is made flying against a headwind with a speed of Vs-VwThe time taken to travel X miles with a tailwind is[tex]t_1=\frac{X}{Vs+Vw}[/tex]The time taken to travel X miles with a headwind is[tex]t_2=\frac{X}{Vs-Vw}[/tex]We know [tex]t_1=t_2-1[/tex] because the return trip is 1 hour longer. Then we have[tex]\frac{X}{Vs+Vw}=\frac{X}{Vs-Vw}-1[/tex]Multiplying by (Vs+Vw)(Vs-Vw)[tex]X(Vs-Vw)=X(Vs+Vw)-(Vs^2-Vw^2)[/tex]Replacing the values of X=875 and Vs=225 we reach a second-degree equation[tex]Vw^2+1750Vw-50625=0[/tex]Which has the following roots:Vw=28.466, Vw=-1778.466We take the positive root and concludeThe wind speed is 28.466 mi/hNote: We can easily check that the first time is 3.45h and the second time is 4.45h.