Question

Against the wind a commercial airline in South America flew 630 miles in 3.5 hours. With a tailwind the return trip took 3 hours. What was the speed of the plane in still air? What was the speed of the wind?

Answer 1

The speed of plane is
`195\ mph`, and speed wind is
`15\ mph`.

Explanation:

Given against the wind the airline flew
`630` miles in
`3.5` hours.

including the tailwind the return trip took
`3` hours.

Let speed of plane is
`x`.

Also, speed of the wind is
`y`.

Now, we will find speed on each case.

Speed against the wind is
`(630)/(3.5)=180\ mph`

Speed with the wind is
`(630)/(3)=210\ mph`

Now, we will write the equation

`x+y=210\\x-y=180`

Add these equation we get,

`2x=390\\x=(390)/(2)\\x=195\ mph`

Now, plug this value in
`x+y=210` to get speed of wind

`195+y=210\\y=210-195\\y=15\ mph`

So, the speed of plane in still air is
`195\ mph`, and speed of the wind is
`15\ mph`.