DIRECT AND INVERSE VARIATION WORPROBLEMS WORKSHEET

Determine whether each situation is an example of a direct variation or inverse variation. Write and equations of variation to represent the situation and solve for the indicated information.

Problem 1 :

The volume V of a gas kept at a constant - temperature varies inversely with the pressure p. If the pressure is 24 pounds per square inch, the volume is 15 cubic feet. What will the volume be when the pressure is 30 pounds per square inch?

Solution

Problem 2 :

The amount of money spent at the gas station varies directly with the number of gallons purchased. When 11.5 gallons of gas were purchased the cost was $37.72. How much would 8 gallons of gas cost?

Solution

Problem 3 :

The time to complete a project varies inversely with the number of employees. If 3 people can complete the project in 7 days, how long will it take 5 people?

Solution

Problem 4 :

The time needed to travel a certain distance varies inversely with the rate of speed. If it takes 8 hours to travel a certain distance at 36 miles per hour, how long will it take to travel the same distance at 60 miles per hour?

Solution

Problem 5 :

The number of centimeters y in a linear measurement varies directly with the number of inches x in the measurement. Pablo's height is 152.4 centimeters or 60 inches. What is Maria's height in centimeters if she is 64 inches tall?

Solution

Problem 6 :

The number of revolutions made by a tire traveling over a fixed distance varies inversely with the radius of the tire. A 12-inch radius tire makes 100 revolutions to travel a certain distance. How many revolutions would a 16-inch radius tire require to travel the same distance?

Solution

Answer Key

1)  Volume of gas is 18.75 cubic feet.

2)  Cost of 8 gallons of gas is $26.24

3)  5 people can complete the project is 4.2 days.

4)  So, it is will 4.8 hours to travel 60 miles

5)  So, Maria's height is 162.56 centimeter.

6)  the required number of revolution is 75.

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