Hello, josh123!
An aircraft with a constant speed in still air travels 3600 km with a constant tailwind in 3 hours.
With the same wind now against the aircraft, it takes 4 hours to make the return trip.
What was the speed of the aircraft in still air, in km/hr?
We will use:
.\(\displaystyle \text{Distance = Speed }\times\text{ Time}\;\;\Rightarrow\;\;\text{Time = }\frac{\text{Distance}}{\text{Speed}}\)
Let \(\displaystyle S\) = speed of aircract in still air (in kph).
Let \(\displaystyle w\) = speed of the wind.
With a tailwind, the aircraft flies faster.
.Its speed is \(\displaystyle S + w\) kph.
. . To fly 3600 km, its time is:
.\(\displaystyle \frac{3600}{S + w}\,=\,3\;\;\Rightarrow\;\;S\,+\,w\:=\:1200\)
. [1]
With a headwind, the aircraft flies slower.
.Its speed is \(\displaystyle S - w\) kph.
. . To fly 3600 km, its time is:
.\(\displaystyle \frac{3600}{s - w}\,=\,4\;\;\Rightarrow\;\;S\,-\,w\:=\:900\)
. [2]
Add [1] and [2] and we get:
.\(\displaystyle 2S\,=\,2100\;\;\Rightarrow\;\;S\,=\,1050\) kph.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
This may strike you as humorous . . . or not.
It turns out that the wind's speed is:
.\(\displaystyle w\,=\,150\) kph.
. . Who is up there flying during a
Catergory 1 hurricane?
