Question

Isolate the variable in a rational equation, multiply each side by the LCD and then solve the resulting equation. (Picture included)

Answer 1

Which employees take the least amount of time at performing either task, folding napkins or setting tables?

Answer 2

a. "Which two employees should the manager ask to SET the tables?"

Look in the column marked "Time to Set ...."
Which two employees set the tables in the shortest period of time?

Answer 3

I got that part it's the other part I'm confused on

Answer 4

Jeff, and Tiffany take the shortest time to set up the tables, meanwhile Stacie and Nick take the least amount of time to fold napkins.

Answer 5

I'm just a little confused on how to figure out part B of task 3. @aum @aaronq

Answer 6

Okay, so first we need to figure out how many seats they need to set up.

45 tables with 4 seats each

45*4=total number of seats

Answer 7

Now, what is gonna take less tim with the combination of the two people doing one of the jobs, folding napkins or setting up?

Answer 8

time*

Answer 9

I think setting up the tables with take less time.

Answer 10

so how long would it take the pair (jeff and tiff) to set up all the tables?

Answer 11

Do I use the total number of seat divided by this to find out how long it would take?

Answer 12

we'll we can do it in several ways. We know what together (Jeff and Tiff) set up 4 seats in 5 minutes.

So per table they take \(\dfrac{4~seats}{5~minutes}=0.8~seats/min\) This is a rate.

We know that there are 75*4 seats

so \(time=\dfrac{seats}{rate}=\dfrac{74*5~seats}{0.8~seats/min}\)

Answer 13

So 462.5?

Answer 14

sorry it was supposed to be: \(time=\dfrac{45*4}{0.8}=\dfrac{180}{0.8} =225~min\)

Answer 15

oh okay, that makes more sense.

Answer 16

So, now we go to the napkins, how many napkins have been folded by the other two people in the 225 minutes?

Answer 17

I think it's like 43? Because I followed the same thing that we used before

Answer 18

Wait hold on am I supposed to use the 225 minutes in the equation

Answer 19

yeah

Answer 20

Ok I'm really confused now, I'm coming up with this weird number, could you break it down for me, but without giving me the answer.

Answer 21

Okay, so you need to find the rate of napkin folding

\(\sf rate=\dfrac{\#~of~napkins~folded}{time}\)

then use that rate to find the napkins folded, rearrange the formula

\(\sf napkins~folded=time*rate\)

Answer 22

So \[rate =\frac{ 4 }{ 6.5 }\] then that would make \[6.5 * 0.61 = 3.965\]

Answer 23

but 225 minutes passed, remember?

napkins folded=rate*time= \(\dfrac{4}{6.5}seats/min*225~min\)

Answer 24

So it would be \[\frac{ 4 }{ 6.5 } = 0.61 \] then it would be \[0.61 * 225 \]

Answer 25

yes

Answer 26

So the answer is 137.25?

Answer 27

I rounded up 0.615 to 0.62 and got 139.5

If you didn't round at all, you'd get 138.461 seats

so i would go with 138 seats

Now, how many napkins to fold out of the total are there?

Answer 28

Do I divided or multiply to find this?

Answer 29

subtract 138 from the total

Answer 30

and what the total?

Answer 31

What's*

Answer 32

45*4= 180

Answer 33

So 42?

Answer 34

great. So now, after the 225 min. All 4 people are folding napkins. Whats the rate now?

Answer 35

I would divide right?

Answer 36

I just noticed we make a mistake. Give min and i'll correct it, i have to step out

Answer 37

Okay no problem

Answer 38

So the problem is that the rates were supposed to be doubled, because there are 2 people working there are 8 napkins/tables set per time interval.

So the first rate was rate=\(\dfrac{8~seats}{5~min}=1.6~seats/min\)

time to finish setting up all seats=\(\dfrac{45*4}{1.6~seats/min}=112.5~min\)

In that time, the number of napkins folded was :

napkins folded=time*rate=112.5 min*\(\dfrac{8}{6.5~min}\)=138.46153=138 napkins

(which now that i see, it only made a difference in the time.)

The number of napkins left is = 45*4-138=42 napkins

Now that 4 people (all) are working on folding the napkins.

The rate is: \(rate=\dfrac{16~napkins}{(3+4+5+3.5)~min}=\dfrac{16}{15.5}=1.0322\approx 1~napkin/min\)

can you find how long it will take to fold the rest (42 napkins)?

Answer 39

So I would divide the number of napkins by the rate?

Answer 40

If one person can finish a job in 'a' minutes and a second person can finish the same job in 'b' minutes, then together they can finish the job in: \(\Large \frac{1}{\frac 1a + \frac 1b}\) minutes or in \(\Large \frac{ab}{a+b}\) minutes.
If four people, working separately, can each finish a job in 'a', 'b', 'c' and 'd' minutes respectively, then together they can finish the job in: \(\Large \frac{1}{\frac 1a + \frac 1b + \frac 1c + \frac 1d}\) minutes.

It is evident from the data that setting tables will finish earlier than folding napkins because 2+3 min. < 3+3.5 min. Therefore, let us first calculate how long it will take to set all 45 tables.

Tiffany can set places in a table in 2 minutes.
Jeff can set places in a table in 3 minutes.
Together they can set places in ONE table in: \(\Large \frac{2~*~3}{2~+~3} = \large 1.2\) minutes.
Together they can set places in 45 tables in: \(\large 45 * 1.2 = 54\) minutes.

Stacie can finish folding napkins in a table in 3 minutes.
Nick can finish folding napkins in a table in 3.5 minutes.

Together they can finish folding napkins in ONE table in: \(\Large \frac{3~*~3.5}{3~+~3.5} = \large 1.62\) minutes.
Working together how many tables can they finish in 54 minutes?
\(\Large \frac{54}{1.62} = \large 33.33 \) tables. That leaves \(\large 45 - 33.33 = 11.67 \) tables left.


Stacie, Jeff, Tiffany and Nick working together can finish folding napkins in ONE table in \(\Large \frac{1}{\frac 13 + \frac 14 + \frac 15 + \frac {1}{3.5}} = \large 0.94\) minutes. Together they can finish folding napkins in the remaining tables in \(\large 0.94~*~11.67 = 10.97 \approx 11\) minutes.

Total time = \(\large 54 + 11 = 65\) minutes.