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.

Divide your first equation by 5 to get : x+y = 600

Divide your 2nd equation by 10 to get: x-y = 300

add them: 2x = 900
x = 450
sub that back into your new 1st
450 + y = 600
y = 150

To determine the algebraic equation for 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 denote the speed of the plane in still air as 'p' and the speed of the wind as 'w'.

From the given information,
1st plane: 5(x+y) = 3000
2nd plane: 10(x-y) = 3000

The equation 5(x+y) = 3000 represents the distance traveled by the plane with the wind in 5 hours. Since the plane's speed is increased by the wind's speed, we add them together.

Similarly, the equation 10(x-y) = 3000 represents the distance traveled by the plane against the wind in 10 hours. In this case, we subtract the wind's speed from the plane's speed since it is flying in the opposite direction.

Now, let's simplify these equations:

5(x+y) = 3000
=> x + y = 600 (Divide both sides by 5)

10(x-y) = 3000
=> x - y = 300 (Divide both sides by 10)

We now have a system of two equations with two unknowns: x + y = 600 and x - y = 300.

To solve this system of equations, we can use the method of elimination. By adding the two equations, we can eliminate the 'y' term:

(x + y) + (x - y) = 600 + 300
=> 2x = 900 (Combine like terms)

Dividing both sides by 2 gives us:

x = 450

Now, substitute the value of x back into one of the original equations, such as x + y = 600, to find the value of y:

450 + y = 600
=> y = 600 - 450
=> y = 150

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

Therefore, the algebraic equation to determine when the planes will meet is:

Distance = Speed x Time

Using the speed and time, you can calculate the distance traveled by each plane. When the distances are the same, the planes will meet.