Question 1

It takes the owner/operator of a dog kennel 6 hr to clean all of the cages. It takes his assistant 2 hr more than that to clean the same cages. How long will it take if they work together?
 __________ hr

Accepted Answer

The answer of It takes the owner/operator of a dog...

Question 2

The equation $y = k x$ defines __________ variation.

Accepted Answer

The answer of The equation $y = k x$ defines...

Question 3

If one printer can complete a job in 32 minutes and a second printer can finish the same print job in 48 minutes, how long will it take to complete the print job if the second printer starts 2 minutes after the first printer started?

Accepted Answer

The answer of If one printer can complete a job...

Question 4

It takes a grounds keeper 45 minutes to prepare a softball field for a game. It takes his assistant 55 minutes to prepare the same field. How long will it take if they work together to prepare the field?
 _________ min

Accepted Answer

The answer of It takes a grounds keeper 45 minutes...

Question 5

Hazel can weed her flower bed in 4 hours and Melissa can do it in 2 hours. If they work together, how long will it take to seed the flower bed?

Accepted Answer

The answer of Hazel can weed her flower bed in...

Question 6

One crew can put up holiday decorations in the mall in 6 hours. A second crew can put up the decorations in 5 hours. How long will it take if both crews work together to decorate the mall?
 __________ hr

Accepted Answer

The answer of One crew can put up holiday decorations...

Question 7

Princess Allison can fill the moat around her enchanted castle in 6 hours and her evil wicked stepsister could fill it in 8 hours. Princess Allison's godmother said if they worked together they would live happily ever after. How long would it take to fill the moat if they work together?

Accepted Answer

The answer of Princess Allison can fill the moat around...

Question 8

Solve the proportion. $\frac { n ^ { 2 } } { 6 } = \frac { n } { n + 1 }$

Accepted Answer

The answer of Solve the proportion. \(\frac { n ^...

Question 9

Solve the problem by writing a variation model. The costs of a trucking company vary jointly with the number of trucks in service and the number of hours they are used. When 3 trucks are used for 7 hours each, the costs are $1,533. Find the costs of using 9 trucks, each for 13 hours.

Accepted Answer

The answer of Solve the problem by writing a variation...

Question 10

Solve the proportion. $\frac { r - 2 } { 5 } = \frac { r } { 7 }$

Accepted Answer

The answer of Solve the proportion. \(\frac { r -...

Question 11

The Washington Monument shown below casts a shadow of $169 \frac { 1 } { 2 }$ feet at the same time as a 5-foot-tall tourist casts a shadow of $1 \frac { 1 } { 2 }$ feet. Find the height of the monument.

Accepted Answer

The answer of The Washington Monument shown below casts a...

Question 12

Solve the problem by writing a variation model. The number of days that a given number of bushels of corn will last when feeding cattle varies inversely as the number of animals. If x bushels will feed 27 cows for 10 days, how long will the feed last for 10 cows?

Accepted Answer

The answer of Solve the problem by writing a variation...

Question 13

Express the verbal model " P varies directly with the square of a and inversely with the cube of j " into symbols.

Accepted Answer

The answer of Express the verbal model " P varies...

Question 14

Out of a sample of 250 women's blouses, 10 were rejected because of a missing button. How many blouses would you expect to have a missing button in a run of 600 shirts?

Accepted Answer

The answer of Out of a sample of 250 women's...

Question 15

In a scale drawing, a 280-foot antenna tower is drawn $7 \frac { 1 } { 2 }$ inches high. The building next to it is drawn $2 \frac { 1 } { 4 }$ inches high. How tall is the actual building?

Accepted Answer

The answer of In a scale drawing, a 280-foot antenna...

Question 16

Solve the problem by writing a variation model. An object in free fall travels a distance s that is directly proportional to the square of the time t . If an object falls 960 feet in 8 seconds, how far will it fall in 10 seconds?

Accepted Answer

The answer of Solve the problem by writing a variation...

Question 17

Solve the proportion. $\frac { 1 } { x + 2 } = \frac { - 2 x } { x + 3 }$

Accepted Answer

The answer of Solve the proportion. \(\frac { 1 }...

Question 18

Express the verbal model in symbols. x varies inversely as the cube of v .

Accepted Answer

The answer of Express the verbal model in symbols. x...

Question 19

Solve the problem by writing a variation model. The distance that a car can go varies directly with the number of gallons of gasoline it consumes. If a car can go 300 miles on 12 gallons of gasoline, how far can it go on a full tank of 17 gallons?

Accepted Answer

The answer of Solve the problem by writing a variation...

Question 20

A monument casts a shadow of 175 feet at the same time as a 6-foot tall person casts a shadow of 1.5 feet. How tall is the monument?

Accepted Answer

The answer of A monument casts a shadow of 175...

Quiz 6: Rational Expression and Equations

It takes the owner/operator of a dog kennel 6 hr to clean all of the cages. It takes his assistant 2 hr more than that to clean the same cages. How long will it take if they work together? __________ hr

The equation y=kxy = k xy=kx defines __________ variation.

If one printer can complete a job in 32 minutes and a second printer can finish the same print job in 48 minutes, how long will it take to complete the print job if the second printer starts 2 minutes after the first printer started?

It takes a grounds keeper 45 minutes to prepare a softball field for a game. It takes his assistant 55 minutes to prepare the same field. How long will it take if they work together to prepare the field? _________ min

Hazel can weed her flower bed in 4 hours and Melissa can do it in 2 hours. If they work together, how long will it take to seed the flower bed?

One crew can put up holiday decorations in the mall in 6 hours. A second crew can put up the decorations in 5 hours. How long will it take if both crews work together to decorate the mall? __________ hr

Princess Allison can fill the moat around her enchanted castle in 6 hours and her evil wicked stepsister could fill it in 8 hours. Princess Allison's godmother said if they worked together they would live happily ever after. How long would it take to fill the moat if they work together?

Solve the proportion. n26=nn+1\frac { n ^ { 2 } } { 6 } = \frac { n } { n + 1 }6n2​=n+1n​

Solve the problem by writing a variation model. The costs of a trucking company vary jointly with the number of trucks in service and the number of hours they are used. When 3 trucks are used for 7 hours each, the costs are $1,533. Find the costs of using 9 trucks, each for 13 hours.

Solve the proportion. r−25=r7\frac { r - 2 } { 5 } = \frac { r } { 7 }5r−2​=7r​

The Washington Monument shown below casts a shadow of 16912169 \frac { 1 } { 2 }16921​ feet at the same time as a 5-foot-tall tourist casts a shadow of 1121 \frac { 1 } { 2 }121​ feet. Find the height of the monument.

Solve the problem by writing a variation model. The number of days that a given number of bushels of corn will last when feeding cattle varies inversely as the number of animals. If x bushels will feed 27 cows for 10 days, how long will the feed last for 10 cows?

Express the verbal model " P varies directly with the square of a and inversely with the cube of j " into symbols.

Out of a sample of 250 women's blouses, 10 were rejected because of a missing button. How many blouses would you expect to have a missing button in a run of 600 shirts?

In a scale drawing, a 280-foot antenna tower is drawn 7127 \frac { 1 } { 2 }721​ inches high. The building next to it is drawn 2142 \frac { 1 } { 4 }241​ inches high. How tall is the actual building?

Solve the problem by writing a variation model. An object in free fall travels a distance s that is directly proportional to the square of the time t . If an object falls 960 feet in 8 seconds, how far will it fall in 10 seconds?

Solve the proportion. 1x+2=−2xx+3\frac { 1 } { x + 2 } = \frac { - 2 x } { x + 3 }x+21​=x+3−2x​

Express the verbal model in symbols. x varies inversely as the cube of v .

Solve the problem by writing a variation model. The distance that a car can go varies directly with the number of gallons of gasoline it consumes. If a car can go 300 miles on 12 gallons of gasoline, how far can it go on a full tank of 17 gallons?

A monument casts a shadow of 175 feet at the same time as a 6-foot tall person casts a shadow of 1.5 feet. How tall is the monument?

The equation $y = k x$ defines __________ variation.

Solve the proportion. $\frac { n ^ { 2 } } { 6 } = \frac { n } { n + 1 }$

Solve the proportion. $\frac { r - 2 } { 5 } = \frac { r } { 7 }$

In a scale drawing, a 280-foot antenna tower is drawn $7 \frac { 1 } { 2 }$ inches high. The building next to it is drawn $2 \frac { 1 } { 4 }$ inches high. How tall is the actual building?

Solve the proportion. $\frac { 1 } { x + 2 } = \frac { - 2 x } { x + 3 }$