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Any questions?

We want to know the distance, so we plug the right numbers into the formula:

500 x 12 = 6,000 miles

500 x 10 = 5,000 miles.

So a pilot would cut 1,000 miles off of their trip by using the Great Circle Route.

Example time!

The Answer

Let's say we want to go from Duluth to Paris. The true distance is about 5,000 miles. The Great Circle route is about 4,500 miles. If a plane is going 500 mph, how long would it take the plane to get to France going either way?

The Answer!

Dividing the distance by the rate will give us the time it takes us to get to France.

5000 / 500 = 10 hours.

4500 / 500 = 9 hours.

In this case, the Great Circle Route is 500 miles shorter than the true distance route, making it one hour shorter.

Hint: We should take the distance and divide it by the rate we are going. 5,000/500 and 4,500/500.

This time, we want to find speed, so we will divide distance by time in order to find the answer.

8000 / 20 = 400 Miles per hour

7200 / 18 = 400 Miles per hour

So the speeds are the same, but obviously the Great Circle Route saved a couple hours on our trip!

Another one

We are now leaving Duluth for Seoul, South Korea! The true distance is 8,000 miles. The Great Circle Route is 7,200 miles. If it takes 20 hours flying the true distance, and 18 hours going the Great Circle Route, what is the speed of the plane?

Why does it work?

We are going from Duluth to Moscow. If a plane is going 500 mph for 12 hours along the true distance route, and 500 mph for 10 hours on the Great Circle Route, how much shorter is the Great Circle Route going to be?

Which formula should we use?

Rate x Time = Distance

The circumference of the earth shrinks as we travel over / near the poles.

The Great Circle only works if we travel to a place on the opposite side of the world.

The Great Circle

The Great Circle is an imaginary line following the curvature of the Earth.

It's the shortest distance between two points on a sphere. Since it's the shortest point, it's often used by pilots to save fuel when traveling.

Just kidding... Here are some useful formulas for solving Great Circle Problems:

Distance = Rate x Time or d = r x t

Time = Distance / Rate or t = d / r

Rate = Distance / Time or r = d / t

Points to Ponder...

  • What is a Great circle?
  • Why is it important?
  • Yes... math might be used today (but it's simple, I swear!)
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