Question

A pilot flies 640 miles with a tail wind of 35 miles per hour. Against the wind, he flies only 455 miles in the same amount of time. Find the rate of the plain in still air

Answer 1

recall your d = rt, distance = rate * time.

so, we know the wind rate is 35mph.

when the pilot goes with it, it runs for say "t" hours and covers 640 miles.

when he goes against it, it runs for say also "t" hours, covering 455 miles only.

now, let's say the still air speed of the plane is "r", so when it goes with the wind, is not really going "r" mph, is really going "r + 35", because the wind is adding speed.

likewise, when it goes against it, the speed is not "r" but "r - 35", the wind is slowing it down.


`\bf \begin{array}{lcccll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{t}\\ &------&------&------\\ \textit{with wind}&640&r+35&t\\ \textit{against the wind}&455&r-35&t \end{array} \\\\\\ \begin{cases} 640=t(r+35)\implies \cfrac{640}{r+35}=\boxed{t}\\\\ 455=t(r-35)\\ ----------\\ 455=\left( \boxed{(640)/(r+35)} \right)(r-35) \end{cases}`


`\bf 455(r+35)=640(r-35)\implies 455r+15925=640r-22400 \\\\\\ 38325=185r\implies \cfrac{38325}{185}=r\implies \cfrac{7665}{37}=r\implies 207(6)/(37)=r`