Applications of Rational Functions

Bob can mow a yard in 5 hours and Jeff can mow the same lawn in 3 hours. Which equation could be used to solve an equation to find the time it would take to mow the yard if they both mowed the lawn at the same time.

• $\frac{1}{3}+\frac{1}{5}+x=1$

• $\frac{x}{5}+\frac{1}{3}=1$

• $\frac{1}{5}+\frac{x}{3}=1$

• $\frac{x}{3}+\frac{x}{5}=1$

Tags

CCSS.HSA.CED.A.3

Sally needs a 10% acid solution for an experiment. She has 3 mL of 18% acid solution. How much water does Sally need to mix in with the 18% solution to obtain the 10% solution? Which equation could be used to model this situation?

• (.18)3+(.10)(x) = 0(x+3)

• (.18)3+0(x)=.10(3+x)

• (.18)3+0x=.10

• (.18)3+.10(x+3)=0(x)

Tags

CCSS.HSA.CED.A.3

It takes Roger 2 hours to paint a room. It takes Erin 3 hours to paint the same size of room. Which equation could be used to solve to find the time it would take to paint the room if they painted together.

• $\frac{1}{3}+\frac{1}{2}=6x$

• $\frac{x}{3}+\frac{x}{2}=6$

• $\frac{x}{3}+\frac{x}{2}=1$

• $\frac{x}{3}+\frac{x}{2}=6x$

Tags

CCSS.HSA.CED.A.1

You need to create a 12 ounce mixture of 60% antifreeze. How much pure antifreeze should you mix with 40% antifreeze in order to obtain the mixture that you need? Which equation could be used to illustrate this problem?

• 1x + .4(x)=.60(x+12)

• 1x + .40(12-x)=.60(12)

• 1(12-x) + .4(x)=.60(12)

• 1x + .4(12)=.60 (x+12)

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.REI.B.3

You need a 15% apple juice solution for a certain test. The only solutions you have already are 10% apple juice solution and 30% solution. You need 10 liters of the 15% acid solution. How many liters of 10% solution and 30% solution should you use?

• 1.5 Liters of 30% 
  8.5 Liters of 10%
• 2.5 Liters of 30% 
  7.5 Liters of 10% 
• 30 Liters of 30%
  10 Liters of 10%
• .5 Liters of 30%
  .2 Liters of 10%

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.2

CCSS.HSA.REI.C.6

Tim can paint the football field in 8 hours. JaQuii can paint the football field in 6 hours. Damien can paint the field in 4 hours. How long does it take them to paint the field together? 

• It will take them 24 hours. 
• It will take them 1.8 hours. 
• It will take them 11 hours. 
• It will take them 2.4 hours. 

Tags

CCSS.HSA.CED.A.1

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

• 48 minutes
• 50 minutes
• 24 minutes
• 12 minutes

Tags

CCSS.HSA.CED.A.1

Catherine can paint a house in 15 hours. Dan can paint a house in 30 hours. How long will it take them working together.

• 20 hours
• 10 hours
• 22 hours
• 17 hours

Tags

CCSS.HSA.CED.A.1

Igor can do a job in 20 minutes. Fred can do the same job in 30 minutes. How long will the job take if they both work together?

• 15 minutes
• 22 minutes
• 25 minutes
• 12 minutes

Tags

CCSS.HSA.CED.A.1

How many ounces of 30% acid solution should be mixed with 40 ounces of 2% acid solution to make 5% acid solution?

• 1.2 ounces

• 12 ounces

• 2 ounces

• 4.8 ounces

Tags

CCSS.8.EE.C.7B