Question

A plane can travel 1880 miles in 4 hours. When the plane flies the opposite direction, against the wind it takes 5 hours to fly the same distance. Find the rate of the plane in still air and the rate of wind

Answer 1

Let the speed of plane be "x" and the speed of wind be "w".

Going with the wind, the rate of plane is

`x+w`

Going against the wind, the rate of plane is

`x-w`

We also know the distance formula, which is

`D=RT`

Where

D is distance

R is rate

T is time

From the given information, we can write >>>>

`\begin{gathered} 1880=(x+w)4 \\ 4x+4w=1880 \end{gathered}`

and,

`\begin{gathered} 1880=(x-w)5 \\ 5x-5w=1880 \end{gathered}`

We can now solve both the equations simultaneously to find the value of "x" and "w".

Let's multiply the first equation by "5" and the second equation by "4". Then, we will add both equations and find the value of "x" first. All the steps are shown below:

`\begin{gathered} 4x+4w=1880 \\ 5x-5w=1880 \\ ---------- \\ 5*\lbrack4x+4w=1880\rbrack \\ 4*\lbrack5x-5w=1880\rbrack \\ ---------- \\ 20x+20w=9400 \\ 20x-20w=7520 \\ ---------- \\ 40x=16,920 \\ x=(16,920)/(40) \\ x=423 \end{gathered}`

Now, we will take this value of "x" and substitute into the first equation and figure out the value of "w". Shown below:

`\begin{gathered} 4x+4w=1880 \\ 4(423)+4w=1880 \\ 1692+4w=1880 \\ 4w=188 \\ w=(188)/(4) \\ w=47 \end{gathered}`Answer

Rate of Plane in still air = 423 miles per hour

Rate of Wind = 47 miles per hour