Direct Variation
This is the formula for direct variation
y= kx
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?
87.5 km
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?
6.75 hours
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?
0.8 miles
If y varies directly as x, and y = 3 when x = 9, find x when y = 5.
15
Y varies inversely as x and y = 2 when x = 8. Find y when x = 32
1/2
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?
6 amperes
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. (round off to whole number)
859
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.
$190.65
y varies directly as x squared and y = 16 when x =4. Find y when x = 12.
144
y varies inversely with x. If y = 7 when x = -4, find y when x = 5.
-28/5
Hooke’s law states that the distance d that a spring is stretched by a hanging object varies directly as the mass m of the object. If the distance is 20 cm when the mass is 3 kg, what is the distance when the mass is 8 kg?
160/3 or 53.3 cm
The frequency of a vibrating string varies inversely as its length. A string 3 feet long vibrates 175 cycles per second. Find the frequency of a 5 foot string.
105 cycles per second
y varies directly with x. If y = 15 when x = -18, find y when x = 8/5.
-4/3
If y varies inversely as x, and y = 39 when x = 3, find y when x = 11.
117/11
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 with a mass of 50 kg?
100/3 or 33.3 kg
The volume V of gas varies inversely to the pressure P. The volume of a gas is 200 cubic cm under pressure of 32 kg/square cm. What will be its volume under pressure of 40 kg/square cm?
160 cubic cm
y varies directly as x cubed. if y = 375 when x = 5, find y when x = 3.
81
x varies inversely as y cubed. x is 16 when y is 5. Find x when y is 2.
250
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?
1600 ft
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?
7.6 hours