The force, F, with which you must loosen a bolt, is inversely proportional to the length, L, of the wrench. A wrench that is 5 inches long requires 300 pounds of force. Which of the following equations is the best model of this situation?

A. F = 1500 L
Correct! Force times length gives the constant of variation, so (300)(5) = 1500. Because this situation is an inverse variation, the equation is in the correct form.

B. F = 1500L
Incorrect. Although the constant of variation is correct, the equation is in the format of a direct variation.

C. F = 60L
Incorrect. This equation represents the situation as a direct variation instead of an inverse variation.

D. F = 60 L
Incorrect. The constant of variation is incorrect.

The time it takes to build a certain fence varies inversely with the number of people who are building it. If four people can build the fence in 8 hours, how long would it take 6 people to do the same job?

A. 5 hours 20 minutes
Correct! The equation that models this situation is t = 32/p. Dividing 32 by 6 people means it would take 5 1/3 hours to build the fence.

B. 5 hours 33 minutes
Incorrect. Although it would take 5.3333 hours to build the fence, one-third of an hour is 20 minutes.

C. 12 hours
Incorrect. It will take less time, not more, to build the fence when more people are working.

D. 9 hours 30 minutes
Incorrect. It will take less time, not more, to build the fence when more people are working.

The distance that a car traveling at 55 miles per hour covers is directly proportional to the amount of time that it has moved at that speed. Which equation best models this situation?

A. d = 55 t
Incorrect. Time and distance are related directly and this equation models an inverse variation.

B. d = 55t
Correct! Fifty-five miles per hour multiplied by the time equals the distance traveled.

C. dt = 55
Incorrect. Time and distance are related directly and this equation models an inverse variation.

D. t = 55 d
Incorrect. Time and distance are related directly and this equation models an inverse variation.

Elizabeth knows that if she does not work, she does not make any money. If she works 35 hours she earns $546.00. She earns $312.00 for working 20 hours. What type of variation does this situation model have? What is the constant of variation and what does it mean in this situation?

A. This situation is a direct variation. The constant of variation is 15.6 and means Elizabeth earns $15.60 per hour.
Correct! The points (0, 0), (20, 312), and (35, 546) are linear and are a direct variation. The slope of the line is the constant of variation, and this rate of change would be the amount of money she earns every hour.

B. This situation is a direct variation. The constant of variation is 27.5 and means Elizabeth works an average of 27.5 hours.
Incorrect. The points (0, 0), (20, 312), and (35, 546) are linear and are a direct variation. However, the slope of the line is the constant of variation, and would be the amount of money she earns every hour.

C. This situation is an inverse variation. The constant of variation is 15.6 and means Elizabeth earns $15.60 per hour.
Incorrect. The points (0, 0), (20, 312), and (35, 546) are linear and are a direct variation. An inverse variation does not contain (0, 0).

D. This situation is an inverse variation. The constant of variation is 429 and means Elizabeth earns an average of $429.00 per pay check.
Incorrect. The points (0, 0), (20, 312), and (35, 546) are linear and are a direct variation. An inverse variation does not contain (0, 0).