if a plane can travel 450 miles per hour with the wind and 410 miles per hour against the wind, find the speed of the plane without a wind and speed of the wind?

***i know the speed is 230 but i cant get the wind speed HELP****

Question

if a plane can travel 450 miles per hour with the wind and 410 miles per hour against the wind, find the speed of the plane without a wind and speed of the wind?

***i know the speed is 230 but i cant get the wind speed HELP****

anonymous · Answer

When you are flying with the wind, it adds to your speed, and when you are flying against it, it takes away from it.

Let's call the Speed of the Plane 'x' and the Speed of the Wind 'y'.

Therefore we know that 
x + y = 450
and 
x - y = 410

anonymous · Answer

You then get either x or y by itself, plug in and simply to find the answer.

For example:

x - y = 410
x = y + 410

and then we plug that into x + y = 450 to get
x + y = 450
(y + 410) + y = 450
2y + 410 = 450
2y = 40
y = 20

anonymous · Answer

Remembering that we found x to be equal to (y + 410) can now use the value of y to find the value of x.

x = y + 410
y = 20
x = 20 + 410
x = 430

So x is 430 and y is 20, therefore the Speed of the Plane is 430 and the Speed of the Wind is 20

anonymous · Answer

The average speed, the speed without the wind is the sum of (450+410)/2 or 430mph.
The wind speed is 450-430 or 20mph.