# Worksheet: Direct Variation and its Applications

Q1:

The velocity, , of an object in m/s is directly proportional to the time, , in seconds. This relationship can be expressed in the equation . Find the value of when m/s.

Q2:

Which of the following relations represent a direct variation between the two variables and ?

• A
• B
• C
• D

Q3:

A car moves at a uniform velocity and travels 240 km in 3 hours. If the car continues at the same velocity, what distance will be covered in 5 hours?

Q4:

A car moves with a uniform velocity where the distance varies directly with time. If the car travels a distance of 231 km in 9 hours, how far will it travel in 15 hours?

Q5:

Mr. Earl used 40 pounds of insecticide to cover 1 360 square feet of lawn and 70 pounds to cover an additional 2 380 square feet. How many pounds of insecticide would Mr. Earl need to cover his whole lawn of 5 066 square feet?

Q6:

A gas station charges \$3 per gallon for gasoline, and \$6 for a car wash. Carl never washes his car there because he thinks it is too expensive, but he often buys gasoline there. Is the total money he spends at the station directly proportional to the amount of gasoline he buys?

• Ayes
• Bno

Q7:

The length of a rectangle is 8 m and its width is 5 m. What is the perimeter of a similar rectangle with length 19 meters?

• A m
• B m
• C m
• D m
• E m

Q8:

Victor works 37 hours a week and is paid \$416.25. Given that , the amount in dollars that Victor earns, varies directly with , the number of hours he works, write an equation for in terms of .

• A
• B
• C
• D
• E

Q9:

The amount a babysitter earns varies directly with the number of hours they work. A babysitter earns \$25.50 for 3 hours of babysitting.

How much would they earn for 2 hours of babysitting?

Write an equation for , the number of dollars earned for hours of babysitting.

• A
• B
• C
• D
• E

Q10:

If varies directly with and when , what is the value of when ?

Q11:

If varies directly with and when , find the value of when .

Q12:

Mark is 1.6 m tall, and his shadow is 4 m long. He is standing near a tree whose shadow is 22 m long.

How tall is the tree?

Q13:

The cost of hiring a small car for 4 days is \$170. What would the cost to hire the car for a week at the same rate be? Give your answer to two decimal places if necessary.

Q14:

Given that varies directly with , and when , write an equation for in terms of .

• A
• B
• C
• D
• E

Q15:

Given that varies directly as , write an equation for in terms of using as a non-zero constant.

• A
• B
• C
• D

Q16:

Given that varies directly with , and when , write an equation for in terms of .

• A
• B
• C
• D
• E

Q17:

Given that varies directly with , and when , write an equation for in terms of .

• A
• B
• C
• D
• E

Q18:

Helen uses cups of flour to make 20 cookies. She makes a second batch using cups of flour to make 30 cookies. Is the amount of flour she uses directly proportional to the number of cookies she bakes?

• Ayes
• Bno

Q19:

Use the data in the table to find the values of and .

 136 204 884 1 360 70 420 455 700
• A,
• B,
• C,
• D,
• E,

Q20:

Which table does NOT show varying directly with ?

• A 2 4 6 1.5 3 4.5
• B 2 0 8 0
• C 5 3 1 6 10 30
• D 10 20 30 2 4 6
• E 1 2 3 12 24 36

Q21:

The amount of stain needed to cover a wooden surface is directly proportional to the area of the surface. If 4 pints are required to cover a square deck of side 3 feet, how many pints of stain are needed to paint a square deck of side 8 feet 3 inches?

• A pints
• B pints
• C pints
• D11 pints
• E pints