Rational Equations and Their Applications

This video tutorial covers the application of rational equations through two examples. The first example involves calculating the time it takes for two people to complete a task individually when working together. The second example involves determining the speeds of a passenger train and a freight train given their travel distances and time. The video explains how to set up and solve rational equations, emphasizing the importance of understanding rates and proportions.

If one person can complete a task 8 hours sooner than another, and together they finish it in 3 hours, how long does it take the slower person to complete the task alone?

• 16 hours

• 12 hours

• 10 hours

• 14 hours

What is the rate of work per hour for a person who takes 6 hours to complete a task?

• 1/4 of the task

• 1/5 of the task

• 1/6 of the task

• 1/7 of the task

In the equation 0 = X^2 - 14X + 24, what are the possible values of X?

• X = 10 or X = 4

• X = 12 or X = 2

• X = 14 or X = 0

• X = 16 or X = -2

Why is X = 2 considered an extraneous solution in the first problem?

• Because it is less than 0

• Because it is greater than 12

• Because it is not a real number

• Because it results in a negative time

What is the relationship between the speeds of the passenger train and the freight train?

• The passenger train is 10 mph faster

• The passenger train is 12 mph faster

• The passenger train is 14 mph faster

• The passenger train is 16 mph faster

If the passenger train travels 330 miles in the same time the freight train travels 270 miles, what is the speed of the freight train?

• 52 mph

• 50 mph

• 54 mph

• 56 mph

What equation represents the relationship between distance, rate, and time?

• Distance = Rate + Time

• Distance = Rate / Time

• Distance = Rate x Time

• Distance = Time / Rate

How do you solve a proportion equation involving two rates and distances?

• By dividing the rates

• By cross-multiplying

• By subtracting the distances

• By adding the rates

What is the speed of the passenger train if the freight train's speed is 54 mph?

• 64 mph

• 66 mph

• 68 mph

• 70 mph

Why is it important to verify the solution after solving for a variable?

• To check if the solution is a whole number

• To confirm the solution answers the question

• To ensure the solution is positive

• To verify the solution is less than 100