Word Problems Involving Quadratic Equations

In summary, an engineer needs help solving a problem where he can decrease the time it takes to travel 200km by 2 hours. To find the original speed of the freight train, the engineer needs to increase the speed by 5km per hour. This can be translated into the equation v(t-2)=200, where v is the original speed and t is the time it takes to travel 200km.
  • #1
Equilibrium
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hey can you help me solve these, I've got 20 problems..and i only need is this
problem so that i have an idea of answering the others

An engineer can decrease by 2 hours the time it takes to travel 200km. If he increases the speed of the freight train by 5km per hour, what is the original speed of the train?
 
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  • #2
Let S be the original speed of the train.

If he travels a distance of 200km in T hours, can you write down an expression for the speed S ?
 
  • #3
Translate the word problem into mathematics. Let's call the original speed of the train v (km/h) and the time it takes t (hours).
So he travels 200 km in t hours at a speed v:

vt=200

If he increases v by 5 km/h, he can travel 200 km in t-2 hours. How would you tranlsate that into an equation?

Doh, Fermat beat me to it.
 
  • #4
Great minds think alike :smile:
 

FAQ: Word Problems Involving Quadratic Equations

What is a quadratic equation?

A quadratic equation is an algebraic equation in the form of ax^2 + bx + c = 0, where x represents an unknown variable and a, b, and c are constants. The highest power of x in a quadratic equation is 2, which is why it is called a quadratic equation.

How do I solve a word problem involving quadratic equations?

To solve a word problem involving quadratic equations, you first need to identify the unknown variables and write them in terms of x. Then, set up the equation using the given information and solve for x using factoring, the quadratic formula, or completing the square. Finally, plug in the value of x to find the solution to the word problem.

What are the different methods for solving quadratic equations?

The three main methods for solving quadratic equations are factoring, the quadratic formula, and completing the square. Factoring involves finding common factors and using the zero product property to solve for x. The quadratic formula is a formula that provides the solutions for x in terms of the coefficients of the equation. Completing the square is a method of manipulating the equation to create a perfect square trinomial, which can then be solved for x.

How do I know if a word problem involves a quadratic equation?

A word problem involves a quadratic equation if it can be written in the form of ax^2 + bx + c = 0. Look for keywords such as "area", "height", "width", "maximum", "minimum", "velocity", "acceleration", or "distance" in the word problem, as these can indicate the use of a quadratic equation.

Can quadratic equations be used in real life situations?

Yes, quadratic equations can be used to solve real life problems involving motion, such as calculating the maximum height of a ball thrown in the air or finding the optimal dimensions for a rectangular garden. They can also be used in finance, engineering, and science to model and analyze various scenarios.

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