If a plane can travel 470 miles per hour with the wind and 430 miles per hour against the​ wind, find the speed of the wind and the speed of the plane in still air.

Question

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Part 1
What is the speed of the​ wind?
  

Answer 1

Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".

Given that the plane can travel 470 miles per hour with the wind, we can write the equation:

p + w = 470

And given that the plane can travel 430 miles per hour against the wind, we can write the equation:

p - w = 430

To solve for the speed of the wind, we need to eliminate one of the variables. We can do this by adding the two equations together:

(p + w) + (p - w) = 470 + 430

2p = 900

Dividing both sides by 2, we get:

p = 450

Now that we have the speed of the plane in still air, we can substitute it back into one of the original equations to solve for the speed of the wind.

Using the equation p + w = 470:

450 + w = 470

Subtracting 450 from both sides:

w = 20

So the speed of the wind is 20 miles per hour.

Therefore, the speed of the plane in still air is 450 miles per hour.