sample work problems with solutions and ways in solving them.. Enjoy!!! and please do thank me for uploading this.... your welcome!!!!

1. Suppose one paintercanpaintthe entire house intwelvehours,andthe secondpaintertakeseight
hours.How longwouldittake the two painterstogethertopaintthe house?
If the firstpaintercando the entire jobintwelve hoursandthe second paintercando it ineighthours,
then(thishere isthe trick!) the firstguycan do1/12 of the jobperhour, andthe secondguycan do 1/8
perhour. Howmuch thencan theydo perhour if theyworktogether?
To findouthow muchtheycan dotogetherper hour,I add togetherwhattheycan do individuallyper
hour: 1/12 + 1/8 = 5/24. Theycan do 5/24 of the jobper hour.Now I'll let"t" standfor how longthey
take to do the jobtogether.Thentheycan do 1/t perhour, so5/24 = 1/t. Flipthe equation,andyouget
that t = 24/5 = 4.8 hours.That is:
hoursto complete job:
firstpainter:12
secondpainter:8
together:t
completedperhour:
firstpainter:1/12
secondpainter:1/8
together:1/t
addingtheirlabor:Copyright© ElizabethStapel 1999-2011 All RightsReserved
1/12 + 1/8 = 1/t
5/24 = 1/t
24/5 = t
Theycan complete the jobtogetherinjustunderfive hours.
As youcan see inthe above example,"work"problemscommonlycreate rational equations.Butthe
equationsthemselvesare usuallyprettysimple.
One pipe can fill apool 1.25 timesfasterthana secondpipe.Whenbothpipesare opened,theyfill the
pool infive hours.Howlongwouldittake to fill the pool if onlythe slowerpipe isused?
Convertto rates:
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hoursto complete job:
fastpipe:f
slowpipe:1.25f

2. together:5
completedperhour:
fastpipe:1/f
slowpipe:1/1.25f
together:1/5
addingtheirlabor:
1/f + 1/1.25f = 1/5
multiplyingthroughby5f:
5 + 5/1.25 = f
5 + 4 = f = 9
Then1.25f = 11.25, so the slowerpipe takes11.25 hours.
If you're notsure how I derivedthe rate forthe slow pipe,thinkaboutitthisway:If someone goestwice
as fast as you,thenyoutake twice as longas he does;if he goesthree timesasfast, thenyoutake three
timesaslong.In thiscase,if he goes1.25 timesasfast, thenyoutake 1.25 timesaslong.
It takes1.5 hoursfor Timto mow the lawn.Lindacan mow the same lawnin2 hours.How longwill it
take Johnand Linda,worktogether,tomow the lawn?
SolutiontoProblem1:
We firstcalculate the rate of workof John andLinda
John:1 / 1.5 andLinda 1 / 2
Let t be the time forJohnand Lindato mow the Lawn. The work done byJohnalone isgivenby
t * (1 / 1.5)
The work done byLinda alone isgivenby
t * (1 / 2)
Whenthe two worktogether,theirworkwill be added.Hence
t * (1 / 1.5) + t * (1 / 2) = 1
Multiplyall termsby6

3. 6 (t* (1 / 1.5) + t * (1 / 2) ) = 6
and simplify
4 t + 3 t = 6
Solve fort
t = 6 / 7 hours = 51.5 minutes.
Problem2:
It takes6 hoursfor pumpA, usedalone,tofill atankof water.PumpB usedalone takes8 hoursto fill
the same tank. We want to use three pumps:A,B and anotherpumpC to fill the tankin2 hours.What
shouldbe the rate of pumpC? How longwouldittake pumpC, usedalone,tofill the tank?
SolutiontoProblem2:
The rates of pumpsA and B can be calculatedasfollows:
A: 1 / 6 and B: 1 / 8
Let R be the rate of pumpC. Whenworkingtogetherfor2 hours,we have
2 ( 1 / 6 + 1 / 8 + R ) = 1
Solve forR
R = 1 / 4.8 , rate of pumpC.
Let t be the time ittakespumpC, usedalone,tofill the tank.Hence
t * (1 / 4.8) = 1
Solve fort
t = 4.8 hours, the time it takespumpC to fill the tank.
Problem3: A tank can be filledbypipe A in5 hoursand bypipe B in8 hours,each pumpworkingonits
own.Whenthe tank isfull anda drainage hole isopen,the waterisdrainedin20 hours.If initiallythe
tank wasemptyand someone startedthe twopumpstogetherbutleftthe drainage holeopen,how
longdoesittake forthe tankto be filled?
SolutiontoProblem3:

4. Let's firstfindthe ratesof the pumpsandthe drainage hole
pumpA: 1 / 5 , pump B: 1 / 8 , drainage hole:1 / 20
Let t be the time forthe pumpsto fill the tank.The pumps,addwaterintothe tankhoweverthe
drainage hole drainswateroutof the tank,hence
t ( 1 / 5 + 1 / 8 - 1 / 20) = 1
Solve fort
t = 3.6 hours.
Problem4: A swimmingpool canbe filledbypipe A in3 hoursand by pipe B in6 hours,eachpump
workingonitsown.At 9 am pumpA isstarted.At whattime will the swimmingpool be filledif pumpB
isstartedat 10 am?
SolutiontoProblem4:
the rates of the two pumpsare
pumpA: 1 / 3 , pump B: 1 / 6
Workingtogether,If pumpA worksfor t hours thenpumpB workst - 1 hourssince itstarted1 hour late.
Hence
t * (1 / 3) + (t - 1) * (1 / 6) = 1
Solve fort
t = 7 / 3 hours = 2.3 hours = 2 hours20 minutes.
The swimmingpool will be filledat
9 + 2:20 = 11:20
Work rate × Time to finishthe job= 1 jobdone
Work rate = (1 job done) /(Time tofinishthe job)
Time of doingthe job = (1 job done) /(Workrate)
For example
Albertcanfinisha jobinA days
Bryan can finishthe same jobinB days
Carlocan undothe jobin C days

5. 1/A = rate of Albert
1/B = rate of Bryan
1/C = rate of Carlo
AlbertandBryan worktogetheruntil the jobisdone:(1/A + 1/B)t = 1
Albertisdoingthe jobwhile Carloisundoingituntil the jobisdone:(1/A - 1/C)t = 1
Problem
Lejoncan finishajobin 6 hours while Romel candothe same jobin 3 hours.Workingtogether,how
manyhours can theyfinishthe job?
Solution
Hide Clickhere toshowor hide the solution
Rate of Lejon= 1/6
Rate of Romel = 1/3
$(1/6 + 1/3)t = 1$
$frac{1}{2}t= 1$
$t = 2 , text{hours}$ answer
Case 2: Workershave equal rates
Work load= no.of workers× time tofinishthe job
Work done = no. of workers× time of doingthe job
To finishthe job
Work done = Work load
If a jobcan be done by10 workersin5 hours,the work loadis10(5) = 50 man-hours.If 4 workersis
doingthe jobfor 6 hours,the workdone is4(6) = 24 man-hours.A remainingof 50 - 24 = 26 man-hours
of workstill needstobe done.
Problem

6. Elevenmencouldfinishthe jobin15 days.Five menstartedthe joband fourmenwere addedat the
beginningof the sixthday.Howmanydayswill ittake themto finishthe job?
Solution
Hide Clickhere toshowor hide the solution
Work load= 11(15) = 165 man-days
Work done in5 days= 5(5) = 25 man-days
Let $x$ = no.of daysfor themto finishthe job
$25 + (5 + 4)(x - 5) = 165$
$25 + 9(x - 5) = 165$
$9x = 185$
$x = 20.56 ,text{days}
Solve. Simplify all fraction answers and use simple "improper" form. For
example, if you get 1 2
/4, write 3/2.
Decimal form 1.5 is also acceptable.
1. If 6 workers can harvest a field in 18
hours, how many workers would it
have taken to do it in 3 hours?
workers
2. If 8 workers can plant a garden in 6
hours, how many workers would it
have taken to do it in 4 hours?
workers
Complexity=1, Mode=hours
Solve. Simplify all fraction answers and use simple "improper" form. For
example, if you get 1 2
/4, write 3/2.
Decimal form 1.5 is also acceptable.
1. Peter and Steven take 51
/3 hours to do
a job. Steven alone takes 16 hours to
do the same job. How long would it
take Peter to do the same job alone?
hours
2. Jennifer takes 4 hours to do a job.
John takes 6 hours to do the same
job. Working together, how many
hours will it take them to do the job?
hours
Complexity=1, Mode=rates
Solve. Simplify all fraction answers and use simple "improper" form. For
example, if you get 1 2
/4, write 3/2.
Decimal form 1.5 is also acceptable.

7. 1. Mary works 2.5 times faster
than Peter. Together, they do a
job in 12.5 hours. How long
does it take Mary working alone
to do the same job?
hours
2. One pipe can empty a tank 5 times faster than
another pipe can fill the tank. Starting with a
full tank, if both pipes are turned on, it takes
10 hours to empty the tank. How long does it
take the slower pipe working alone to fill an
empty tank?
hours
Complexity=1, Mode=mixed
Solve. Simplify all fraction answers and use simple "improper" form. For
example, if you get 1 2
/4, write 3/2.
Decimal form 1.5 is also acceptable.
1. One pipe can empty a tank 5.5 times
faster than another pipe can fill the
tank. Starting with a full tank, if both
pipes are turned on, it takes 16.5 hours
to empty the tank. How long does it
take the slower pipe working alone to
fill an empty tank?
hours
2. One pipe can empty a tank 2.5 times
faster than another pipe. Starting
with a full tank, if both pipes are
turned on, it takes 7.5 hours to
empty the tank. How long does it
take the faster pipe working alone to
empty a full tank?
hours
Answers
Complexity=1, Mode=man-hours
Solve. Simplify all fraction answers and use simple "improper" form. For
example, if you get 1 2
/4, write 3/2.
Decimal form 1.5 is also acceptable.
# Problem
Correct
Answer
Your
Answer
1
If 6 workers can harvest a field in 18 hours, how many
workers would it have taken to do it in 3 hours?
36
workers
Solution
Let x be the number of workers it would have taken.
(6 workers)(18 hours) = (3 hours)x
108 worker-hours = 3x hours
36 workers = x

8. # Problem
Correct
Answer
Your
Answer
2
If 8 workers can plant a garden in 6 hours, how many
workers would it have taken to do it in 4 hours?
12
workers
Solution
Let x be the number of workers it would have taken.
(8 workers)(6 hours) = (4 hours)x
48 worker-hours = 4x hours
12 workers = x
Complexity=1, Mode=hours
Solve. Simplify all fraction answers and use simple "improper" form. For
example, if you get 1 2
/4, write 3/2.
Decimal form 1.5 is also acceptable.
# Problem
Correct
Answer
Your
Answer
1
Peter and Steven take 51
/3 hours to do a job. Steven alone
takes 16 hours to do the same job. How long would it take
Peter to do the same job alone?
8
hours
Solution
Let t = number of hours for Peter working alone
1 job
t
+
1 job
16 hours
=
1 job
51
/3 hours
Answer: t = 8 hours
# Problem
Correct
Answer
Your
Answer
2
Jennifer takes 4 hours to do a job. John takes 6 hours to do the
same job. Working together, how many hours will it take them
to do the job?
12/5
hours
Solution
Let t = number of hours working together
1 job
4 hours
+
1 job
6 hours
=
1 job
t
Answer: t = 12
/5 hours

9. Complexity=1, Mode=rates
Solve. Simplify all fraction answers and use simple "improper" form. For
example, if you get 1 2
/4, write 3/2.
Decimal form 1.5 is also acceptable.
# Problem
Correct
Answer
Your
Answer
1
Mary works 2.5 times faster than Peter. Together, they do a job
in 12.5 hours. How long does it take Mary working alone to do
the same job?
17.5
hours
Solution
Let f = number of hours it takes Mary working alone
and 2.5f = number of hours it takes Peter working alone
1 job
f
+
1 job
2.5f
=
1 job
12.5 hours
Solve for f to get f = 17.5 hours
Working alone, Mary takes f.
Answer: f = 17.5 hours
# Problem
Correct
Answer
Your
Answer
2
One pipe can empty a tank 5 times faster than another pipe can
fill the tank. Starting with a full tank, if both pipes are turned on,
it takes 10 hours to empty the tank. How long does it take the
slower pipe working alone to fill an empty tank?
40
hours
Solution
Let f = number of hours it takes the faster pipe and 5f = number of hours it takes the
slower pipe
1 tank
f
-
1 tank
5f
=
1 tank
10 hours
Solve for f to get f = 8 hours
Working alone, the slower pipe takes 5f.
Answer: 5f = 40 hours
Complexity=1, Mode=mixed
Solve. Simplify all fraction answers and use simple "improper" form. For
example, if you get 1 2
/4, write 3/2.
Decimal form 1.5 is also acceptable.

10. # Problem
Correct
Answer
Your
Answer
1
One pipe can empty a tank 5.5 times faster than another pipe can
fill the tank. Starting with a full tank, if both pipes are turned on,
it takes 16.5 hours to empty the tank. How long does it take the
slower pipe working alone to fill an empty tank?
74.25
hours
Solution
Let f = number of hours it takes the faster pipe and 5.5f = number of hours it takes
the slower pipe
1 tank
f
-
1 tank
5.5f
=
1 tank
16.5 hours
Solve for f to get f = 13.5 hours
Working alone, the slower pipe takes 5.5f.
Answer: 5.5f = 74.25 hours
# Problem
Correct
Answer
Your
Answer
2
One pipe can empty a tank 2.5 times faster than another pipe.
Starting with a full tank, if both pipes are turned on, it takes 7.5
hours to empty the tank. How long does it take the faster pipe
working alone to empty a full tank?
10.5
hours
Solution
Let f = number of hours it takes the faster pipe and 2.5f = number of hours it takes
the slower pipe
1 tank
f
+
1 tank
2.5f
=
1 tank
7.5 hours
Solve for f to get f = 10.5 hours
Working alone, the faster pipe takes f.
Answer: f = 10.5 hours