Solving Linear Equations: 2 Planes from LAX - Cbarker1

In summary, two planes starting from Los Angeles International Airport fly in opposite directions. The second plane starts $\frac{1}{2}$ hour after the first plane, but is 80 kilometers per hour faster. After 2 hours, the planes are 3200 kilometers apart. Using x to represent the speed of the first plane and y to represent the speed of the second plane, we can set up a system of linear equations to solve for the airspeed of each plane.
  • #1
cbarker1
Gold Member
MHB
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Dear Everyone,

I have some help setting up a system of linear equation. The problem states,
Two planes start from Los Angeles International Airport and fly in opposition directions. The second plane starts $\frac{1}{2}$ hour after the first plane, but its speed is 80 kilometers per hour faster. Find the airspeed of each plane if 2 hours after the first plane departs, the planes are 3200 kilometers apart.

I know the x is the first plane and y is the second plane.

Thank you

Cbarker1
 
Last edited:
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  • #2
Cbarker1 said:
Dear Everyone,

I have some help setting up a system of linear equation. The problem states,
Two planes start from Los Angeles International Airport and fly in opposition directions. The second plane starts $\frac{1}{2}$


$\frac12$ what? What are the units?

after the first plane, but its speed is 80 kilometers per hour faster. Find the airspeed of each plane if 2 hours after the first plane departs, the planes are 3200 kilometers apart.
I know the x is the first plane and y is the second plane.

Thank you

Cbarker1
 

FAQ: Solving Linear Equations: 2 Planes from LAX - Cbarker1

What are linear equations?

Linear equations are mathematical equations that describe a relationship between two variables, typically represented by x and y. They follow the form y = mx + b, where m is the slope and b is the y-intercept.

How do you solve linear equations?

To solve a linear equation, you need to isolate the variable on one side of the equation by using inverse operations. This means that whatever operation is being done to the variable, you do the opposite operation to both sides of the equation. For example, if the equation is 3x + 7 = 22, you would subtract 7 from both sides first, then divide by 3 to isolate x.

What is the significance of 2 planes in solving linear equations?

In the context of the given scenario, the two planes represent two different equations with two variables (x and y). By finding the point of intersection between these two planes, we can determine the solution to the system of equations and solve for the values of x and y.

Why is it important to use specific points like LAX in solving linear equations?

Using specific points like LAX (Los Angeles International Airport) in the given scenario allows us to plug in known values for x and y into the equations and solve for the other variable. This helps to narrow down the possible solutions and make the process of solving linear equations more efficient.

Can linear equations be used to model real-world situations?

Yes, linear equations can be used to model and solve real-world situations, such as predicting the growth of a population or calculating the cost of a phone plan. They are commonly used in fields such as physics, economics, and engineering to describe and analyze relationships between variables.

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