Question

A graphic designer and her assistant working together can complete an advertising layout in 6 days. The assistant working alone could complete the job in 16 more days than the designer working alone. How long would it take each person to do the job?

Answer 1

so the amount of time it takes the designer to do a job is 1/1

the assisstant will do 1/17 of it in the same amount of time, right?

Answer 2

if the job done together is done in 6 days that means the designer did 6 parts to the assistants 6/17 parts

Answer 3

where did 1/17 come from?

Answer 4

i'm supposed to declare variables and have equations and pellet

Answer 5

and pellet*

Answer 6

its the information in the posted problem;

it takes 16 more days to finish the same amount of work;
D = 1 day done
A = 1 + 16 days done

Answer 7

the ratio is 1 to 17 then; right?

Answer 8

its takes the assistant alone 16 more days than it would take the designer working alone..

Answer 9

i see, i read it wring :)

Answer 10

lol okay! you were confusing me for a minute!

Answer 11

The assistant working alone could complete the job in 16 more days than the designer working alone.

D = D days

A = D+16 days

add them together and we get:

2D + 16 days to do 2 of the same jobs right? im thinking here

Answer 12

2D + 16 would be done in 12 days then ... that make sense?

Answer 13

D = # of days designer could do it alone
A = # of days Assistant could do it alone
?

Answer 14

yes, it was either that or come up with something that would just confuse the situation :)

Answer 15

okay; so one equation would be:
a=2d+16
what would the other one be?

Answer 16

a+d=6 ?

Answer 17

A+D = 6, yes if we knew what A and D where .... but all we know is what it is if they workd alone. right?

Answer 18

but when they work together; they can complete it in 6 days.

Answer 19

right, so lets assume they do 2 of the same jobs; they would finish in 12 days correct?

Answer 20

yea

Answer 21

So if D can finish in D days on one job; let her do that job alone

A can finish the other job in D+16 days, so let A do the other one .... is my thinking

Answer 22

D + (D+16) = 12 days for 2 jobs then, and this might be more work then needed, but to me it makes sense

Answer 23

i'm not following

Answer 24

let me try to see if this is going to work first, then ill try to describe it if it does :)

Answer 25

haha okay.

Answer 26

2d + 16 = 12 days

2d+16
------ = 1 days work ; reduce
12

d + 8
----- = 1 days work
6

d/6 + 8/6

maybe, and i cant be sure yet, the A does the same amount of wok in 1' 1/3 the time it takes D to do it

Answer 27

6/8 = .75, of the work the D does ....

.25 + .75 = 1, and thats done in 6 days; but how does this measure against the rest of it?

Answer 28

i wish this made more sense to me than a gut feeling :)

Answer 29

2d+16=12 : where is that coming from?

Answer 30

D=8 days; then A = 24 days if im gutting it right

1/8 + 1/24 = 4/24; 24/4 = 6 all right

Answer 31

spose we have 2 jobs to do in 12 days; since 6 days * 2 = 12

Answer 32

why not just a=d+16 though?

Answer 33

because to me, that tells us nothing in the outcome of things; that is just a relative measure and nothing that can be quantified with a single job. We have to set up an experiment to measure against.

Answer 34

in other words, that is related to just this one job and we cant determine, or at least i cant determine what to measure it against ..

Answer 35

we know that alone it will take 16 more days to finish alone, than it does with help.

we know that D can finish it alone in ..... some time frame that is undetermined

Answer 36

Without being able to establish the timeframe for D how do we measure another 16 days from it?

Answer 37

give D and A their own workspace to measure against; 2 jobs that would have taken them 12 days to complete if worked together, and D works one, while A works the other for comparison

Answer 38

Job = D = 6days
Job = D+16 = 6days

2Jobs = 2D+16 = 12days; reduce by 2

Job = D + 8 = 6 days; divide by 6 to see how much is done in 1 day

1/6 Job = D/6 + 8/6 = 1 day .... we are getting somewhere now

Answer 39

these are percentages of work done in the day;

6/D and 6/8 are the speed with which the work relative to each other, and the faster one HAS to be the Designer.

6/8 = 3/4 = .75 = 75%; leaving 25% for the Assistant

Answer 40

the rest of this is hard to put into words ... but im trying :)

Answer 41

I think you are doing a great job!!

Answer 42

... thnx :)

Answer 43

\[\frac{6}{D}:\frac{6}{8},\ D=8\]
but why?

Answer 44

would it be the same if the length was 5 extra days?

2d+5 = 12

(2d+5)/12 = 1

12/2d = 12/5; d = 5/2 = 2.5 A = 7.5

6(1/2.5 + 1/7.5) = 3.2 ..... so it seems to be a fluke

Answer 45

thats the best i got fer tonite, good luck with it :)

Answer 46

How does this work?
A=16+G; G=graphic designer and A=assistant
A+G=6; so we can plug A in there
(16+G)+G=6
16+2G=6
2G=-10
G=-5, hmmm I dont think we can have a neg amount of days, we could plug this in to find A
A=16+(-5)
A=11

Answer 47

I don't know, it was just a thought :)

Answer 48

Here:
Designer working alone takes t days
Assistant takes t +16 days
Together they work for 6 days;
\[6/t+6/(t+16)=1\]
clear the denominators and combine terms:
\[6(t+16) + 6t=t(t+16)\]
\[t^2+4t-96=0\]
\[(t+12)(t-8)=0\]
t must be 8 (positive time to complete job for designer
Designer takes 8 days
Assistant takes 24 days
Together they take 6
\[6/8+6/24=1\]

Answer 49

Solve the following for x, the time required for the graphic designer to complete the layout solo.\[\frac{1}{x+16}+\frac{1}{x}= \frac{1}{6}\]x=8, x+16 = 24