Direct Inverse Variations

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

• 8 painters

• 10 painters

• 9 painters

• 11 painters

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

The cost per person to rent a mountain cabin varies inversely to the number of people who share the rent. If the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?

• $22.50

• $57.60

• $4.50

• $12.50

The gallons of water used to take a shower varies directly with the number of minutes in the shower. If an 8 minute shower uses 48 gallons of water, find the constant of variation.

• 1/6

• 6

• 8

• 48

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

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

Given: y varies inversely with x. If y = 40 when x = 16, find x when y = -5.

Find the value of k.

Given: y varies inversely with x. If y = 40 when x = 16, find x when y = -5. Find the value of x.