Question is: What is the algebraic equation to determine when they will meet?

For the following information, I understand 5(x+y) = 3000 for 1st plane & 10(x-y) = 3000 for 2nd plane.

When an airplane flies with a given wind, it can travel 3000 km in 5hrs. When the same airplane flies in the opposite direction against the wind it takes 10hrs to fly the same distance. Find the speed of the plane in still air and the speed of the wind.

Vp + Vw = 3000km/5h = 600km/h.

Vp - Vw = 3000km/10h = 300km/h.

Add the 2 Eqs:
Eq1: Vp + Vw = 600.
Eq2: Vp - Vw = 300.
Sum: 2Vp = 900,
Vp = 450km/h = Speed in still air

In Eq1, substitute 450 for Vp:
450 + Vw = 600,
Vw = 150km/h. = Speed of wind.

To determine when the two planes will meet, we need to find the values of the speed of the plane in still air and the speed of the wind.

Let's assign variables to the unknowns:
- Let's represent the speed of the plane in still air as "p"
- Let's represent the speed of the wind as "w"

Given that "5(x+y) = 3000" and "10(x-y) = 3000", we can set up a system of equations to solve for "p" and "w".

1) The first equation is "5(x+y) = 3000". This equation represents the distance the airplane can travel in 5 hours when flying with the wind. Using the distributive property, we can rewrite this equation as "5x + 5y = 3000".

2) The second equation is "10(x-y) = 3000". This equation represents the distance the airplane can travel in 10 hours when flying against the wind. Again, using the distributive property, we can rewrite this equation as "10x - 10y = 3000".

Now we have a system of equations:
- Equation 1: "5x + 5y = 3000"
- Equation 2: "10x - 10y = 3000"

To solve this system, we can use the method of elimination.

Step 1: Multiply equation 1 by 2 to eliminate the y term:
- Equation 1 becomes "10x + 10y = 6000"

Step 2: Add equation 1 and equation 2 together:
- (10x + 10y) + (10x - 10y) = 6000 + 3000
- Simplifying, we get 20x = 9000

Step 3: Solve for x by dividing both sides of the equation by 20:
- x = 9000 / 20
- x = 450

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use equation 1:

5x + 5y = 3000
5(450) + 5y = 3000
2250 + 5y = 3000
5y = 3000 - 2250
5y = 750
y = 750 / 5
y = 150

Therefore, the speed of the plane in still air (p) is 450 km/hr, and the speed of the wind (w) is 150 km/hr.