Maths or physics Interception question

[High_flier]

Two airports (A and B) are 200nm apart. Aircraft 1 leaves airport A and
flies to B at 100kts. Aircraft 2 leaves airport B and flies to A at 200kts.
Both aircraft leave at the same time, where relative to airport A will they
pass each other?

nm=nautical miles
kts=kts

 

[Doc Al]

Here's one way to solve this. Call the time at which they pass each other t. During that time, each flies a certain distance D = V t. So aircraft 1 travels a distance $D_1 = V_1 t$ and aircraft 2 travels a distance $D_2 = V_2 t$. But the total distance traveled by both aircraft must equal the distance between A and B (200 nm). I'll leave the next step to you: set up the equation and solve for t, then plug t into solve for $D_1$.

Once you understand what's happening, you can practically do this problem in your head. Realize that the distance each aircraft travels is proportional to its speed. Aircraft 1 travels half as fast as aircraft 2, so it travels half the distance of aircraft 2. If aircraft 1 travels D, aircraft 2 travels 2D. The total is 3D = 200 nm. Solve for D.

 

[M98Ranger]

In order to solve this interception question, we need to use the formula: Distance = Rate x Time.
First, let's convert the speeds to nautical miles per hour (nmph) since the distance is given in nautical miles.
100 kts = 115.08 nmph
200 kts = 230.15 nmph

Next, we can set up a table to represent the distance each aircraft covers in a certain amount of time:

| Aircraft | Rate (nmph) | Time (hours) | Distance (nm) |
|----------|-------------|--------------|---------------|
| 1 | 115.08 | x | 115.08x |
| 2 | 230.15 | x | 230.15x |

Since both aircrafts leave at the same time, we can set the times equal to each other:
115.08x = 230.15x
Solving for x, we get x = 2.
This means that after 2 hours, both aircrafts will have traveled a certain distance and will pass each other.
To find out where they will pass each other relative to airport A, we can plug in x = 2 into the distance formula:
Aircraft 1: 115.08 x 2 = 230.16 nm
Aircraft 2: 230.15 x 2 = 460.3 nm
Therefore, they will pass each other 230.16 nm from airport A.
In conclusion, after 2 hours, both aircrafts will pass each other 230.16 nm from airport A.