ProblemAt full speed, Hal travels 600 miles in 2 hourswith the wind. The same distance againstthe wind takes 3 hours.What's the maximum speed of Hal's airplanein still air? What's the speed of the wind?​

Answer: The maximum speed of Hal's airplane in still air is:[tex]v= 250\ miles/h[/tex]The speed of the wind[tex]c = 50\ miles/h[/tex]Step-by-step explanation:Remember that the velocity v equals the distance d between time t.[tex]v=\frac{d}{t}[/tex]  and [tex]t*v=d[/tex]The distance that Hal travels when traveling with the wind is:[tex](2\ hours)(v + c) = 600[/tex] milesWhere v is the speed of Hal and c is the wind speed.The distance when traveling against the wind is:[tex](3\ hours)(v-c) = 600[/tex] milesNow we solve the first equation for v[tex](2)(v + c) = 600[/tex][tex]2v + 2c = 600[/tex][tex]2v= 600-2c[/tex][tex]v= 300-c[/tex]Now we substitute the value of v in the second equation and solve for c[tex]3((300-c)-c) = 600[/tex][tex]3(300-2c) = 600[/tex][tex]900-6c = 600[/tex][tex]-6c = 600-900[/tex][tex]-6c = -300[/tex][tex]6c = 300[/tex][tex]c = 50\ miles/h[/tex]Then:[tex]v= 300-(50)[/tex][tex]v= 250\ miles/h[/tex] The maximum speed of Hal's airplane in still air is:[tex]v= 250\ miles/h[/tex]The speed of the wind[tex]c = 50\ miles/h[/tex]