Confusing math question...or maybe im the confused one...?

Here's how I'd do it... Two hours have passed, right? This means Plane A will be 300 miles north (2x150) and Plane B will be 400 miles west (2x200). Imagine lines drawn between the planes, and from each plane to the departure airport. You have a triangle. You know two of its sides are 400 miles and 300 miles. Use the Pythagorean theorem (a^2+b^2=c^2):

400^2 + 300^2=x^2.

160000 + 90000 = x^2

250000 = x^2

Square root both sides and...

500=x

x=500

There you go! I'd appreciate some points if I was helpful... This took me a pretty long time to write!

The north-bound plane travels 2 hours at a rate of 150 mph. Therefore, the distance traveled would be 300 miles.

The west-bound plane travels also for 2 hours at 200 mph.

Therefore, the distance traveled would be 400 miles.

You have now a right triangle with one side 300, and the other 400.

Using the pythagorean theorem (a^2 + b^2 = c^2)

300^2 + 400^2 = c^2

90000 + 160000 = c^2

250000 = c^2

500 = c, the hypotenuse of the triangle and the distance apart the planes are.

Okay,

if plane 1 travels N at 150 mph for 2 hours, it will be 300 miles North of the airport

plane 2 travels W at 200 mph for 2 hours, so it is 400 miles West of the airport.

Draw a dot to represent the airport. Draw a line coming up to show the path of plane 1. Draw a line going left of the dot to represent plane 2. Now connect the ends of the 2 lines to form a triangle.

Since one side of the triangle = 300, and the other side is 400

a^2 + b^2 = c^2

c = 500, where c is the distance between the 2 planes

Imagine a right triangle. The airplane traveling north at 150 mph hour is side a of the triangle. The airplane traveling west at 200 mph is side b of the triangle. Since a 2-hour time period has passed, multiply both of these values by 2 to get the distances traveled by these two planes. Your two distances should come out to be 300 miles and 400 miles. In order to find the distance between these two airplanes, you need to find the hypotenuse of the right triangle. Use the formula c^2=a^2+b^2. Plug in your values to get c^2=300^2+400^2. Solve for c, and you should get the square root of 250,000, which equals 500 miles. :-D

This is a right triangle problem. Draw a point; this is the airport. Draw a line "north" (up) and a line to the "west" (left). These are the paths of the two airplanes. The one going north goes 150 mph, but since they have been flying for two hours, it has gone 300 miles. Label the line going up as "300". The one going west goes at 200 mph, but again, since it has been two hours, label the line "400". Then, connect two lines. It's a right triangle. Use A squared + B squared = C squared to find the length of the line you just drew. That's the answer.

The first one travels north and the distance of it from the first airport is 150 * (3-1) = 300 miles. The second one travels west and the distance of it from the first airport is 200 * ( 3-1) = 400. You can draw a graph and it looks like a triangle. And you are looking for the longest line which is the distance between 2 planes ( make it d). So d squared = 300 squared + 400 squared. d squared = 90000 + 160000 = 250000. d = root 250000 = 500. The distance is 500 miles.

1:00 to 3:00 is two hours, so one plane is 300 miles north and the other is 400 miles west. Their paths create a right triangle because they were traveling at right angles from each other, so you can use the Pythagorean Theorm (a^2 + b^2 = c^2) to find thier distance apart.

let the distance = d

300^2 + 400^2 = d^2

90,000 + 160,000 = d^2

SQRT(250,000) = SQRT(d^2)

500 = d

So, that is why their distance apart after two hours is 500 miles. I'm sure you will remember this after you read it, it is quite simple.

I hope I un-confused you!

Set up a triangle.

150 mph north will go 300 miles north.

200 mph west will go 400 miles west.

This gives you a right triangle with legs 300, 400 and a hypotenuse of 500.

The planes are 500 miles apart.

Good Luck!

Think 2-dimensionally, not 1-dimensionally.

In other words, if the first plane(plane A) leaves (0,0) on a coordinate plane at 1:00, at 3:00 it will be at (0,300), because it travels 150x2 miles NORTH.

When the second plane (plane B) leaves (0,0) on the same coordinate plane at 1:00, at 3:00 it will be at (-400,0), because it travels 200x2 miles WEST.

The distance between the two planes is therefore, a diagonal line across the second quadrant. If you measure this line, it will be 500 miles. This can be found by either using the distance formula or the Pythagorean theorem.

the one traveling north has gone 300 miles in 2 hours and the one traveling west has gone 400 miles. You just need to sketch out the triangle connecting them with the airport and each other; then use the Pythagorean Theorem