Solving Quadratic Equations and Contextual Problems

The video tutorial explains how to solve a problem involving a family on a road trip. The task is to determine how many miles per hour over the speed limit they must drive to reach their destination in 5.5 hours. The problem is set up by defining variables and formulating an equation based on distance, rate, and time. The tutorial walks through solving a rational equation, simplifying it, and eventually dealing with a quadratic equation. The solution is found using the quadratic formula, and the tutorial concludes by interpreting the results, determining that the family must drive approximately 3.1881 miles per hour over the speed limit.

What is the total distance the family needs to travel during their road trip?

• 70 miles

• 360 miles

• 165 miles

• 195 miles

What variable is used to represent the number of miles per hour over the speed limit?

• y

• z

• x

• t

How is the time to travel a distance calculated in this problem?

• Time equals rate divided by distance

• Time equals distance divided by rate

• Time equals distance times rate

• Time equals rate times distance

What is the least common denominator used to clear the fractions in the equation?

• x plus 55

• x plus 70

• Two times the quantity x plus 55 times the quantity x plus 70

• x plus 55 times x plus 70

What is the first step in solving the equation after clearing the fractions?

• Add the fractions

• Divide the fractions

• Distribute and clear the parentheses

• Multiply the fractions

What type of equation is formed after distributing and combining like terms?

• Linear equation

• Cubic equation

• Quadratic equation

• Exponential equation

Which formula is used to solve the quadratic equation in this problem?

• Binomial theorem

• Quadratic formula

• Factorization method

• Pythagorean theorem

What are the values of a, b, and c in the quadratic formula for this problem?

• a = 11, b = 655, c = -2200

• a = 11, b = 655, c = 2200

• a = 11, b = 720, c = -2200

• a = 11, b = 720, c = 2200

What is the approximate positive solution for x, the number of miles per hour over the speed limit?

• 3.1881

• 62.7335

• 5.5

• 11.5

Why is the negative solution for x not considered in this problem?

• Negative values are not real numbers

• Negative values are not allowed in equations

• Negative speed is not possible

• Negative values do not make sense in this context