Rate of Change and Word Problems

Kathryn is cutting fabric squares for a quilt that she is making her mother for Christmas. She can cut 3 squares in one minute. When her friend taught her how to cut out the squares, however, they cut out 11. Write an equation representing the total number of squares Kathryn will have when she is finished.

• Y = 11X + 3

• Y = 3X + 11

• Y = 11X + 3X

• Y = 3X - 11

Ms. Brown sits down after school to grade a stack of quizzes. She was able to grade 9 in between classes. She grades these quizzes at a rate of 3 per minute. Write an equation to represent the quizzes she grades after school.

• Y = 3X + 9

• Y = 9X + 3

• Y = 3X - 9

• Y = 9X - 3

Abby and Shelby both took after school jobs as checkers at Petco. Abby checks out 9 customers per hour, while Shelby checks out 11 customers per hour. Shelby is running late, however, so by the time she starts checking out customers, Abby has already checked out 7 customers. Write an equation for Abby.

• Y = 11X + 7

• Y = 9X + 11

• y = 9X + 7

• Y = 7X + 9

Chicken Express sell boxes of chicken with varying numbers of pieces. They charge 40 cents for each piece of chicken, plus a fixed charge of 55 cents for the box.

• Y = .55X + .40

• Y=40X + .55

• Y = .40X + .55

• Y = 55X + 40

Ms. Ellison has Algebra tests that need to be graded. Ms. Ellison grades at a rate of 5 per minute. Ms. Ellison has 75 papers to grade. Write an equation to represent how long it will take Ms. Ellison to grade the remaining tests.

• Y = 5X + 75

• Y = 75X + 5

• Y = 75 + 5X

• Y = 75 = 5X

Hudson is already 40 miles away from home on his drive back to college. He is driving 65 mi/h. Write an equation to represent his distance from college.

• y = 40X - 65

• Y = 65X - 40

• Y = 40 X + 65

• Y = 40X - 65

A rocket is 1 mile above the earth in 30 seconds and 5 miles above the earth in 2.5 minutes. What is the rockets rate of change in miles per second? What about miles per second?

Hint: Convert minutes to seconds

A climber is on a hike. After 4 hours he is at an altitude of 800 feet. After 7 hours, he is at an altitude of 950 feet. What is the average rate of change? 

• 200

• 150

• 75

• 50

At 5 seconds, Mrs. Taylor was 10 feet off the ground.  At 11 seconds, she was 34 feet off the ground.  What is her rate in feet per second?

• 5 feet per second

• 2 feet per second

• 4 feet per second

• 6 feet per second

A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water. He is 100 feet below the surface after 40 seconds. What is the scuba divers rate of change?

Write your answer as a fraction.

Mathematical Equivalence

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