Direct and Inverse Variations

The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?

• 5.33 hours 

• 6.75 hours 

• 12 hours 

• 10 hours 

The number of kilograms of water in a person’s body varies directly as the person’s mass.  A person with a mass of 90 kg contains 60 kg of water.  How many kilograms of water are in a person whose mass is 75 kg?

• 50 kg water

• 72 kg water

• 94 kg water

• 150 kg water

In a random sampling of 200 cars of a model, 3 have manufacturing defects. If there is a direct variation between the number of cars and the number of defects, how many of 10,000 cars of the same model will have a manufacturing defect?

• 150

• 200

• 250

• 300

The value of y varies directly with x.  Which function represents the relationship between x and y if y = 14 when x = 6. 

• y=20x

• y=84x

• y=7/3x

• y=3/7x

The sales at a baseball game vary directly with the number of people attending.  If sales for a game are $12,000 when 800 people attend, determine attendance if sales are $30,000

• 1200 people

• 1500 people

• 2000 people

• 2400 people

The variable x is in joint variation with y and z. When the values of y and z are 4 and 6, x is 16. What is the value of x when y = 8 and z =12?

• 32

• 64

• 48

• 96

Suppose p varies directly as r, and p varies inversely as t.
t = 20 when p = 4 and r = 2.
Find t when r = 10 and p = -5.

• 80

• -80

• 4

• -20

The Height of a wave in California varies directly with the seconds that pass by.  At 4 seconds, the wave is 6 feet high.  How many seconds will give you a wave that is 10 feet high? 

• y = 2/3x

• 6

• 6.6

• 7

Is the given table a direct or inverse variation? What is the constant of variation?

• Direct, 12

• Inverse, 12

• Direct, 1/12

• Inverse, 1/12

State what type of variation the equation represents.

• Direct

• Inverse

• Joint

• None