Inverse Variation and Proportionality Concepts

The video tutorial covers inverse variation word problems, focusing on how time and speed are inversely related. It explains the concept using a car speed example, calculates the constant of proportionality, and solves for the speed required to travel in a specific time frame.

What happens to the time taken to travel when the speed of the car increases?

• Time remains constant

• Time increases

• Time decreases

• Time doubles

In an inverse variation, if one variable increases, what happens to the other variable?

• It remains the same

• It decreases

• It increases

• It doubles

What is the general form of the equation for inverse variation?

• y = x/k

• y = k/x

• y = kx

• y = x + k

If the time taken is 8 hours and the speed is 50 mph, what is the constant of proportionality?

• 8

• 400

• 50

• 100

How do you calculate the constant of proportionality in an inverse variation problem?

• Multiply the variables

• Multiply one variable by the constant

• Divide one variable by the other

• Divide the constant by one variable

What is the speed required to travel in 6 hours if the constant of proportionality is 400?

• 100 mph

• 75 mph

• 66.66 mph

• 50 mph

If the constant of proportionality is 400, what is the equation to find the speed for a given time?

• Speed = 400 / Time

• Speed = 400 * Time

• Speed = Time / 400

• Speed = Time + 400

What operation is performed to solve for the unknown speed in the equation 6x = 400?

• Addition

• Subtraction

• Multiplication

• Division

What is the result of dividing 400 by 6 in the context of this problem?

• 66.66

• 50

• 75

• 100

What does the constant of proportionality represent in an inverse variation problem?

• The ratio of the variables

• The product of the variables

• The difference between the variables

• The sum of the variables