A military jet flies directly over and at a right angles to the straight line course of a commercial jet. The military jet is flying 200 mph faster than four times the commercial jet. How fast is each going if they are 2050 miles apart (on a straight line) after one hour?

If this is a right angle why does Henry not use the pythagorean theorum? Since the distances are just the speeds (thanks to the 1 hour) wouldn't it be X^2 + (4x+200)^2 = 2050^2?

Commercial Jet speed = x mi/hr,

Military Jet speed = (4x + 200) mi/hr.

X mi/hr * 1 hr + (4x + 200) mi/hr * 1 hr = 2050,
x + (4x + 200) = 2050,
5x + 200 = 2050,
5x = 2050 - 200 = 1850,
x = 370 mi/hr = commercial jet speed,
4x + 200 = 4 * 370 + 200 = 1680 mi/hr =
military jet speed.

To approach this problem, let's set up some equations.

Let's assume the speed of the commercial jet as "x" mph.

The military jet is flying 200 mph faster than four times the speed of the commercial jet. So, the speed of the military jet can be expressed as "4x + 200" mph.

After one hour, the commercial jet would have traveled a distance of x miles, and the military jet would have traveled a distance of (4x + 200) miles.

Since they are flying at a right angle to each other, we can consider the distance between them as the hypotenuse of a right triangle.

Using the Pythagorean theorem, we can write the following equation:

x^2 + (4x + 200)^2 = 2050^2

Let's solve this equation:

x^2 + 16x^2 + 400x + 40,000 = 4,202,500

Combine like terms:

17x^2 + 400x + 40,000 - 4,202,500 = 0

Simplify:

17x^2 + 400x - 4,162,500 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / (2a)

Using a = 17, b = 400, and c = -4,162,500, we can substitute the values into the formula:

x = (-400 ± √(400^2 - 4 * 17 * -4,162,500)) / (2 * 17)

Calculating the values under the square root:

x = (-400 ± √(160,000 + 283,500,000)) / 34

x = (-400 ± √(283,660,000)) / 34

x = (-400 ± 16,854.87) / 34

Solving for x:

x1 = (-400 - 16,854.87) / 34
x1 = -17,254.87 / 34
x1 = -508.08 (discarding negative value, as speed cannot be negative)

x2 = (-400 + 16,854.87) / 34
x2 = 16,454.87 / 34
x2 = 484.02

Therefore, the speed of the commercial jet is approximately 484.02 mph.

Now, we can find the speed of the military jet by substituting the value of x into our earlier equation:

Speed of military jet = 4x + 200
Speed of military jet = 4 * 484.02 + 200
Speed of military jet = 1,936.08 + 200
Speed of military jet = 2,136.08 mph

So, the military jet is traveling at approximately 2,136.08 mph.

Therefore, the commercial jet is traveling at approximately 484.02 mph and the military jet is traveling at approximately 2,136.08 mph.