Question

a small airplane flies into a headwind for 10 hours Covering a distance of 2000 miles. during the return trip the airlplane has a tailwind and covers the same distance in 8 hours. find the speed of the plane in Still air at the speed of the wind

Answer 1

For the given problem:

Let the speed of the airplane in still air = x

And the speed of the wind = y

when the airplane flies into a headwind for 10 hours Covering a distance of 2000 miles.

So, speed = distance over time

so,

$\begin{gathered} x-y=\frac{2000}{10} \\ x-y=200\rightarrow(1) \end{gathered}$

When the airplane has a tailwind and covers the same distance in 8 hours

so,

$\begin{gathered} x+y=\frac{2000}{8} \\ x+y=250\rightarrow(2) \end{gathered}$

Solve the equations (1) and (2)

Add the equation to cross y, then solve for x:

$\begin{gathered} 2x=200+250 \\ 2x=450 \\ x=\frac{450}{2}=225 \end{gathered}$

substitute with x into equation (2) to find y

$\begin{gathered} 225+y=250 \\ y=250-225 \\ y=25 \end{gathered}$

So, the answer will be:

The speed of the plane in still air = 225 miles per hour

The speed of the wind = 25 miles per hour