Word Problem Do Nows - Math and Science with Dr. Taylor -...

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WordProblemDoNowsMr.Taylor'sMathClass

VariationWordProblems


VariationWordProblems

VariationWordProblems2VariationWordProblems1

DownloadableWorksheet

VariationWordProblems3


DoNow1:

YvariesdirectlyasX.WhenY=2,X=10...

Findk:


DoNow1:

y=kx

DirectVariation:

YvariesdirectlyasX.WhenY=2,X=10...

Findk:


LetsTryAnotherProblem


DoNow2:Theamountofmoneyraisedatacharityfundraiserisdirectlyproportionaltothenumberofattendees.Theamountofmoneyraisedforfiveattendeeswas$100.Howmuchmoneywillberaisedfor60attendees?


DoNow2:

y=kx

DirectVariation:

Theamountofmoneyraisedatacharityfundraiserisdirectlyproportionaltothenumberofattendees.Theamountofmoneyraisedforfiveattendeeswas$100.Howmuchmoneywillberaisedfor60attendees?


DoNow3:

YvarieslinearlywithX.WhenX=0,Y=5.WhenX=3,Y=11.Findtheentireequation.


DoNow3:

YvarieslinearlywithX.WhenX=0,Y=5.WhenX=3,Y=11.Findtheentireequation.

y=kx+C

LinearVariation:


DoNow4:

YvarieslinearlywithX.WhenX=2,Y=15.WhenX=4,Y=23.Findk:


DoNow4:

YvarieslinearlywithX.WhenX=2,Y=15.WhenX=4,Y=23.Findk:

Equation1:

Equation2:

y=kx+C

LinearVariation:


DoNow5:

Supposethatyvariesinverselyasx2andthaty=10whenx=5/2,findthevalueofywhenx=3.


DoNow5:

Supposethatyvariesinverselyasx2andthaty=10whenx=5/2,findthevalueofywhenx=3.

y=k/x2x2k

InverseVariation:


DoNow6:

Supposethatyvariesinverselyasxandthaty=8whenx=3.

a)Formanequationconnectingxandy.

b)Calculatethevalueofywhenx=10.


DoNow6:

Supposethatyvariesinverselyasxandthaty=8whenx=3.

a)Formanequationconnectingxandy.

b)Calculatethevalueofywhenx=10. y=k/x2xk

InverseVariation:


DoNow7:Carldrovefromhishousetoworkatanaveragespeedof35milesperhour.Thedrivetookhim25minutes.Ifthedrivehometookhim30minutesandheusedthesamerouteinreverse,whatwashisaveragespeedgoinghome?


DoNow7:

Carldrovefromhishousetoworkatanaveragespeedof35milesperhour.Thedrivetookhim25minutes.Ifthedrivehometookhim30minutesandheusedthesamerouteinreverse,whatwashisaveragespeedgoinghome?

y=kxz

JointVariation:


DoNow8:

Theforceneededtokeepacarfromskiddingonacurvevariesjointlyastheweightofthecarandthesquareofthespeed,andinverselyastheradiusofthecurve.Ittakes3800poundsofforcetokeepan1800poundcarfromskiddingonacurvewithradius425feetataspeedof45mph.

Whatforceisneededtokeepthesamecarfromskiddingwhenittakesasimilarcurvewithradius450feetat55mph?


DoNow8:

Theforceneededtokeepacarfromskiddingonacurvevariesjointlyastheweightofthecarandthesquareofthespeed,andinverselyastheradiusofthecurve.Ittakes3800poundsofforcetokeepan1800poundcarfromskiddingonacurvewithradius425feetataspeedof45mph.

Whatforceisneededtokeepthesamecarfromskiddingwhenittakesasimilarcurvewithradius450feetat55mph?

y=k/x2zkx2

CombinedVariation:


DoNow9:

zvariesjointlyasxandy,inverselyasw.Writeappropriatecombinedvariationequationandfindzforgivenvaluesx,y,andw.

z=10whenx=5andw=3

z=?whenx=8,y=6andw=12


DoNow9:

zvariesjointlyasxandy,inverselyasw.Writeappropriatecombinedvariationequationandfindzforgivenvaluesx,y,andw.

z=10whenx=5andw=3

z=?whenx=8,y=6andw=12

CombinedVariation:

Equation1:

Equation2:


DoNow10:Bob'sdentistdeterminedthenumberofcavitiesdevelopedinhispatient'smoutheachyearisinverselyproportionaltothetotalnumberofminutesspentbrushingduringeachsession.IfBobdevelopedfourcavitiesduringtheyearinwhichhespentonly30secondsbrushinghisteetheachtime,howmanyannualcavitieswillBobdevelopifheincreaseshisbrushingtimetotwominutespersession?


y=k/x2xk

DoNow10:Bob'sdentistdeterminedthenumberofcavitiesdevelopedinhispatient'smoutheachyearisinverselyproportionaltothetotalnumberofminutesspentbrushingduringeachsession.IfBobdevelopedfourcavitiesduringtheyearinwhichhespentonly30secondsbrushinghisteetheachtime,howmanyannualcavitieswillBobdevelopifheincreaseshisbrushingtimetotwominutespersession?

InverseVariation:


CHALLENGEProblems:


CHALLENGE1:

QvariesasthecuberootofZ.IfQ=9andZ=27,find

1.Theconstantofproportionality

2.AnexpressionforZintermsofQ

3.ThevalueofQwhenZ=8


CHALLENGE2:

ThegravitationalforceFbetweentwosphericalobjects,havingmassm1andm2respectively,variesjointlywithrespecttom1andm2andinverselywithrespecttothesquareofthedistancedbetweenthetwoobjects.Ifm1=20kilograms,m2=100kilogramsandtheforceF=3.35x108Newtonswhenthedistancebetweenthetwoobjectsisd=2meters,findtheconstantofproportionality.

Attachments

WorkWordProblemsWorksheet.pdf

WorkWordProblemsWorksheet.docx

WordProbsWkshtWork.docx

WordProbsWkshtVariation.docx

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Kuta Software - Infinite Algebra 1 Name___________________________________

Period____Date________________Work Word Problems

Solve each question. Round your answer to the nearest hundredth.

1) Working alone, Ryan can dig a 10 ft by 10 ft

hole in five hours. Castel can dig the same

hole in six hours. How long would it take

them if they worked together?

2) Shawna can pour a large concrete driveway

in six hours. Dan can pour the same

driveway in seven hours. Find how long it

would take them if they worked together.

3) It takes Trevon ten hours to clean an attic.

Cody can clean the same attic in seven

hours. Find how long it would take them if

they worked together.

4) Working alone, Carlos can oil the lanes in a

bowling alley in five hours. Jenny can oil

the same lanes in nine hours. If they worked

together how long would it take them?

5) Working together, Paul and Daniel can pick

forty bushels of apples in 4.95 hours. Had

he done it alone it would have taken Daniel

9 hours. Find how long it would take Paul

to do it alone.

6) Working together, Jenny and Natalie can

mop a warehouse in 5.14 hours. Had she

done it alone it would have taken Natalie 12

hours. How long would it take Jenny to do

it alone?

-1-

7 f200l1U24 BKRuhtdaK fSbomfHtvwRaQrseK zLSLNCc.H R SAelkli QrUipgSh0tOsH hr5eksEenrYvIezda.q c 2M6aydle5 zwZi9t2h7 dIFnrfxiDnDiztTeD ZAAlQg6ezbvr2ak 31d.h Worksheet by Kuta Software LLC

7) Rob can tar a roof in nine hours. One day

his friend Kayla helped him and it only took

4.74 hours. How long would it take Kayla

to do it alone?

8) Working alone, it takes Kristin 11 hours to

harvest a field. Kayla can harvest the same

field in 16 hours. Find how long it would

take them if they worked together.

9) Krystal can wax a floor in 16 minutes. One

day her friend Perry helped her and it only

took 5.76 minutes. How long would it take

Perry to do it alone?

10) Working alone, Dan can sweep a porch in

15 minutes. Alberto can sweep the same

porch in 11 minutes. If they worked


11) Ryan can paint a fence in ten hours. Asanji

can paint the same fence in eight hours. If

they worked together how long would it take

them?

12) Working alone, it takes Asanji eight hours to

dig a 10 ft by 10 ft hole. Brenda can dig the

same hole in nine hours. How long would it

take them if they worked together?

-2-

c g2P0n1w2M uK1u0tGaP mSgo1fIt9wKa5rOeS kLALdCY.4 j AA8lBlX 5rliygAh8t7sA TrJevsGeurcvcekdt.H 4 TMhafdFeE HwliutbhA 0IVn8fBiPnDiltOee BAvlAgreob6roaL 31g.a Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 1 Name___________________________________

Period____Date________________Work Word Problems

Solve each question. Round your answer to the nearest hundredth.

1) Working alone, Ryan can dig a 10 ft by 10 ft

hole in five hours. Castel can dig the same

hole in six hours. How long would it take

them if they worked together?

2.73 hours

2) Shawna can pour a large concrete driveway

in six hours. Dan can pour the same

driveway in seven hours. Find how long it

would take them if they worked together.

3.23 hours

3) It takes Trevon ten hours to clean an attic.

Cody can clean the same attic in seven

hours. Find how long it would take them if

they worked together.

4.12 hours

4) Working alone, Carlos can oil the lanes in a

bowling alley in five hours. Jenny can oil

the same lanes in nine hours. If they worked


3.21 hours

5) Working together, Paul and Daniel can pick

forty bushels of apples in 4.95 hours. Had

he done it alone it would have taken Daniel

9 hours. Find how long it would take Paul

to do it alone.

11 hours

6) Working together, Jenny and Natalie can

mop a warehouse in 5.14 hours. Had she

done it alone it would have taken Natalie 12

hours. How long would it take Jenny to do

it alone?

8.99 hours

-1-

A S230r1M2Z BKTuStMas BShoufLt5wbaYrEee OLsL4C7.i 4 7AslWlb ordiJgJhstusl lrbeFsoeOrBvLeOdi.j v 4MOaSdTeo 8wyiKtehx mIrnBfGi2nCi5tie7 xAFl7gZe2bArCa6 E1n.3 Worksheet by Kuta Software LLC

7) Rob can tar a roof in nine hours. One day

his friend Kayla helped him and it only took

4.74 hours. How long would it take Kayla

to do it alone?

10.01 hours

8) Working alone, it takes Kristin 11 hours to

harvest a field. Kayla can harvest the same

field in 16 hours. Find how long it would

take them if they worked together.

6.52 hours

9) Krystal can wax a floor in 16 minutes. One

day her friend Perry helped her and it only

took 5.76 minutes. How long would it take

Perry to do it alone?

9 minutes

10) Working alone, Dan can sweep a porch in

15 minutes. Alberto can sweep the same

porch in 11 minutes. If they worked


6.35 minutes

11) Ryan can paint a fence in ten hours. Asanji

can paint the same fence in eight hours. If

they worked together how long would it take

them?

4.44 hours

12) Working alone, it takes Asanji eight hours to

dig a 10 ft by 10 ft hole. Brenda can dig the

same hole in nine hours. How long would it

take them if they worked together?

4.24 hours

-2-

Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com

SMART Notebook

Work ProblemsName:Period:

1) Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Jordan can dig the same hole in six hours. How long would it take them if they worked together?

2) Shawna can pour a large concrete driveway in six hours. Dan can pour the same driveway in seven hours. Find how long it would take them if they worked together.

3) It takes Trevon ten hours to clean an attic. Cody can clean the same attic in seven hours. Find how long it would take them if they worked together.

4) Working alone, Carlos can oil the lanes in a bowling alley in five hours. Jenny can oil the same lanes in nine hours. If they worked together, how long would it take for them to do the job?

5) Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken Daniel 9 hours. Find how long it would take Paul to do it alone.

6) Working together, Jenny and Natalie can mop a warehouse in 5.14 hours. Had she done it alone it would have taken Natalie 12 hours. How long would it take Jenny to do it alone?

7) Rob can tar a roof in nine hours. One day his friend Kayla helped him and it only took 4.74 hours. How long would it take Kayla to do it alone?

8) Working alone, it takes Kristin 11 hours to harvest a field. Kayla can harvest the same field in 16 hours. Find how long it would take them if they worked together.

9) Working alone, Dan can sweep a porch in 15 minutes. Alberto can sweep the same porch in 11 minutes. If they worked together how long would it take them?

10) Krystal can wax a floor in 16 minutes. One day her friend Perry helped her and it only took 5.76 minutes. How long would it take Perry to do it alone?

Reflection and Extension:

How do you feel about these types of problems? How does the strategy you use to solve these types of problems relate to chemical mixture or percent composition problems?

SMART Notebook

Work ProblemsName:Period:

1) Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Jordan can dig the same hole in six hours. How long would it take them if they worked together?

2) Shawna can pour a large concrete driveway in six hours. Dan can pour the same driveway in seven hours. Find how long it would take them if they worked together.

3) It takes Trevon ten hours to clean an attic. Cody can clean the same attic in seven hours. Find how long it would take them if they worked together.

4) Working alone, Carlos can oil the lanes in a bowling alley in five hours. Jenny can oil the same lanes in nine hours. If they worked together, how long would it take for them to do the job?

5) Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone it would have taken Daniel 9 hours. Find how long it would take Paul to do it alone.

6) Working together, Jenny and Natalie can mop a warehouse in 5.14 hours. Had she done it alone it would have taken Natalie 12 hours. How long would it take Jenny to do it alone?

7) Rob can tar a roof in nine hours. One day his friend Kayla helped him and it only took 4.74 hours. How long would it take Kayla to do it alone?

8) Working alone, it takes Kristin 11 hours to harvest a field. Kayla can harvest the same field in 16 hours. Find how long it would take them if they worked together.

9) Working alone, Dan can sweep a porch in 15 minutes. Alberto can sweep the same porch in 11 minutes. If they worked together how long would it take them?

10) Krystal can wax a floor in 16 minutes. One day her friend Perry helped her and it only took 5.76 minutes. How long would it take Perry to do it alone?



CHALLENGE Problems:

Work Problems: More than Two Persons:

Jane, Paul and Peter can finish painting the fence in 2 hours. If Jane does the job alone she can finish it in 5 hours. If Paul does the job alone he can finish it in 6 hours. How long will it take for Peter to finish the job alone?

Work Problems: Pipes Filling up a Tank:

A tank can be filled by pipe A in 3 hours and by pipe B in 5 hours. When the tank is full, it can be drained by pipe C in 4 hours. if the tank is initially empty and all three pipes are open, how many hours will it take to fill up the tank?

Solutions Resource

SMART Notebook

Variation ProblemsName:Period:

1. Y varies directly as X. When Y = 2, X = 10

Find k:

2. The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. The amount of money raised for five attendees was $100. How much money will be raised for 60 attendees?

3. Y varies linearly with X. When X = 0, Y = 5. When

X = 3, Y = 11.Find the entire equation.

4. Y varies linearly with X.

When X = 2, Y = 15.

When X = 4, Y = 23.

Find k:

(5.)

5. H

6. Suppose that y varies inversely as x and that y = 8 when x = 3.

a) Form an equation connecting x and y.

b) Calculate the value of y when x = 10.

7. Carl drove from his house to work at an average speed of 35 miles per hour. The drive took him 25 minutes. If the drive home took him 30 minutes and he used the same route in reverse, what was his average speed going home?

8. The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the speed, and inversely as the radius of the curve. It takes 3800 pounds of force to keep an 1800 pound car from skidding on a curve with radius 425 feet at a speed of 45 mph.

What force is needed to keep the same car from skidding when it takes a similar curve with radius 450 feet at 55 mph?

9. z varies jointly as x and y, inversely as w. Write appropriate combined variation equation and find z for given values x, y, and w.

z = 10 when x = 5 and w = 3

when x = 8, y = 6 and w = -12, z = ?

10. Bob's dentist determined the number of cavities developed in his patient's mouth each year is inversely proportional to the total number of minutes spent brushing during each session. If Bob developed four cavities during the year in which he spent only 30 seconds brushing his teeth each time, how many annual cavities will Bob develop if he increases his brushing time to two minutes per session?



CHALLENGE Problems:

Q varies as the cube root of Z. If Q=9 and Z=27, find

1. The constant of proportionality

2. An expression for Z in terms of Q

3. The value of Q when Z=8

The gravitational force F between two spherical objects, having mass m1 and m2 respectively, varies jointly with respect to m1 and m2 and inversely with respect to the square of the distance d between the two objects. If m1 = 20 kilograms, m2 = 100 kilograms and the force F = 3.35x108 Newtons when the distance between the two objects is d = 2 meters, find the constant of proportionality.

SMART Notebook

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Word Problem Do Nows - Math and Science with Dr. Taylor -...

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