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Direct Variation
Inverse Variation
Word Problems
Word Problems
Word Problems
100

This is the formula for direct variation

y= kx or y/x=k

100

This is the formula for inverse variation

What is y = k/x or xy=k

100

On a map, distance in km and distance in cm varies directly, and 25 km are represented by 2cm. If two cities are 7cm apart on the map, what is the actual distance between them?

What is 87.5 km

100
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?
What is 6.75 hours
100
Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. If he counted four seconds between the next flash of lightning and thunder, about how far away was the lightning?
What is 0.8 miles
200
If y varies directly as x, and y = 3 when x = 9, find x when y = 5.
What is 15.
200
Y varies inversely as x and y = 2 when x = 8. Find y when x = 32
What is 1/2
200
The electric current I, is amperes, in a circuit varies directly as the voltage V. When 12 volts are applied, the current is 4 amperes. What is the current when 18 volts are applied?
What is 6 amperes
200
Albertson’s found that the demand for Coke products varies inversely as the price of the product. When the price of a Coke product is $2.75, the weekly demand is 1250. Find the weekly demand if the price is raised to $4.00.
What is 859
200
A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. Find the amount of pay for 31 hours of work.
What is $190.65
300

Y is directly proportional to X. y = 16 when x =4. Find y when x = 12.

What is 48.

300

y is inversely proportional to x. If y = 7 when x = 4, find y when x = 28.

What is 1

300

The time taken to cycle a particular distance varies inversely with the speed of the bicycle. Tim takes 3 hours to reach his destination traveling at a constant speed of 12 miles per hour.

Find the constant of proportionality

36 miles

300

The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover. 5 liters of paint can cover a wall with an area of 75 square feet.

Find the constant of proportionality.

1/15

300
A motorboat can travel 20 mi/h in still water. If the boat can travel 3 mi downstream on a river in the same time it takes to travel 2 mi upstream, what is the rate of the river’s current?
What is 4 mph
400

y varies directly with x. If y = 15 when x = 18, find y when x = 1.6.

What is 1.3333...

400
If y varies inversely as x, and y = 39 when x = 3, find y when x = 11.
What is 10.64
400

The time taken to cycle a particular distance varies inversely with the speed of the bicycle. Tim takes 3 hours to reach his destination traveling at a constant speed of 12 miles per hour.

How long would it take Tim to reach his destination if he travels at a constant speed of 15 miles per hour?

2.4 Hours

400

The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover. 5 liters of paint can cover a wall with an area of 75 square feet.

How much paint would be needed to cover an area of 180 square feet?

12 liters

400

A plane flies 910 miles with the wind in the same time it can go 660 miles against the wind. The speed of the plane in still air is 305 miles per hour. What is the speed of the wind?

What is 48.6 mph

500

y varies directly as x. if y = 375 when x = 5, find y when x = 3.

What is 225

500

x varies inversely as y. x is 16 when y is 5. Find x when y is 2.

What is 40

500
Disregarding wind resistance, the distance a body falls from rest varies directly as the square of the time it falls. If a skydiver falls 64 ft in 2 seconds, how far will he fall in 10 seconds?
What is 1600 ft
500
In planning a trip, the time it takes to make the trip varies inversely with the rate of the car. If I take Route A and average 40 mph, it will take 9.5 hours to complete the trip. If I go by Route B and average 50 mph, how long will the trip take?
What is 7.6 hours
500

The circumference, C, of a circle is directly proportional to the diameter, d, of a circle. They are related by the formula C = pi*d.

Find the constant of proportionality in the formula.

pi