Question

A plane flies from City A to City B against The wind in 7 hours. the return trip back to City A with the wind takes only 6 hour. if the distance between City A and City B is 6300 km, find the speed of the plane and still air and the speed of the wind.

Answer 1

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

• With the wind, the speed of plane becomes:

x + w

• Against the wind, the speed of plane becomes:

x - w

We know D = RT, where

D is distance

R is rate

T is time

Going against the wind, it takes 7 hours, so we can write:

`\begin{gathered} 6300=(x-w)7 \\ 7x-7w=6300 \end{gathered}`

Going with the wind, it takes 6 hours, thus:

`\begin{gathered} 6300=(x+w)6 \\ 6x+6w=6300 \end{gathered}`

Let's multiply the first equation by 6 and the second equation by 7:

`\begin{gathered} 6*(7x-7w=6300) \\ 42x-42w=37800 \\ \text{and} \\ 7*(6x+6w=6300) \\ 42x+42w=44100 \end{gathered}`

Adding the two new equations, we can eliminate w and solve for x:

`\begin{gathered} 42x-42w=37,800 \\ 42x+42w=44,100 \\ ---------------- \\ 84x=81900 \\ x=975 \end{gathered}`

We can use this value of x and put it into the first equation and solve for w:

`\begin{gathered} 7x-7w=6300 \\ 7(975)-7w=6300 \\ 6825-7w=6300 \\ 7w=525 \\ w=75 \end{gathered}`

Thus,

Answer

Speed of Plane = 975 km/hr

Speed of Wind = 75 km/hr