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?

The speed of plane is , and speed wind is .

Step-by-step explanation:

Given against the wind the airline flew miles in hours.

including the tailwind the return trip took hours.

Let speed of plane is .

Also, speed of the wind is .

Now, we will find speed on each case.

Speed against the wind is  

Speed with the wind is

Now, we will write the equation

Add these equation we get,

Now, plug this value in to get speed of wind

So, the speed of plane in still air is , and speed of the wind is .

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240