Question

Rick and Debbie are painting a large barn. Debbie paints twice as fast as Rick. They work together for 16 hours and complete the job. Determine how fast Debbie and Rick can paint the entire barn separately

Answer 1

Sorry, there's no diagram or measurements for this, which is why im confused.

Answer 2

do you know how you would set up the equation

Answer 3

Not really.

Answer 4

@AZ

Answer 5

Debbie paints twice as fast as Rick

how would you write that as an equation?


Let's call Debbie as D
and Rick as R

would the equation be

D = 2 * R

or

2 * D = R

Answer 6

uhm.. my brain.

Answer 7

just use numbers

Debbie paints twice as fast as Rick

so if it took Rick took 2 hours to paint

Debbie is twice as fast and she could paint in 1 hour

which equation makes that work if R =2 and D = 1

Answer 8

The first one...?

Answer 9

if R equals 2 and D = 1

and you said the first one

D = 2 * R

put the numbers in

1 = 2 * 2

does that look correct to you?

Answer 10

uh no

Answer 11

wait im- im so confused

Answer 12

what about the second one?

2 * D = R

2 * 1 = 2

Answer 13

does the second equation look correct to you?

Answer 14

what's confusing you?

Answer 15

math

Answer 16

Yeah the second one looks like it would be correct

Answer 17

okay so now we're dealing with the rates at which they complete a job

so Debbie takes D hours to complete the job by herself
and Rick takes R hours to complete the job by himself

following along still?

Answer 18

yes i think

Answer 19

good

so for these kind of questions the equation may seem weird but if you want to understand it, this website can do it much better than I can
(and I don't have the time nor the patience to explain it further unless you'd like me then I can)
https://www.purplemath.com/modules/workprob.htm

Answer 20

but the general form of the equation is

let's say we have two people working
D was how many hours it takes Debbie to complete the job by herself
R was how many hours it takes Rick to complete the job by herself

let's say we have another variable or letter for the amount of time it takes BOTH of them to complete the job. Let's call this letter/variable T

so the equation would be

1/D + 1/R = 1/T

Answer 21

following along still?

Answer 22

yeah

Answer 23

Let me write it like this using the equation tool

\(\dfrac{1}{\text{D}} + \dfrac{1}{\text{R}} = \dfrac{1}{\text{T}}\)

Answer 24

so you can see it better now, alright good

Answer 25

so remember that equation we came up with earlier?

2 * D = R

Answer 26

mhm

Answer 27

so

2D = R

let's plug that into our equation with all the fractions

\( \dfrac{1}{\text{D}} + \dfrac{1}{\text{R}} = \dfrac{1}{\text{T}}\)

so 2D equals R so we can replace R with 2D

\( \dfrac{1}{\text{D}} + \dfrac{1}{\text{2D}} = \dfrac{1}{\text{T}}\)

Answer 28

Now look back at your question again

It said
`They work together for 16 hours and complete the job`

16 is the time it took for BOTH of them to complete the job
that means 16 is our T

so we have

\( \dfrac{1}{\text{D}} + \dfrac{1}{\text{2D}} = \dfrac{1}{\text{16}}\)

Answer 29

does all that make sense still?

Answer 30

Yeah, I just have to read over it a couple times for me to understand it.

Answer 31

once you've read it over a few times, let me know if you end up with any questions

also take a look at that link I sent

Answer 32

and then we can continue with finding the answer

Answer 33

Okay, I think I'm caught up now.

Answer 34

good so we had

\( \dfrac{1}{\text{D}} + \dfrac{1}{\text{2D}} = \dfrac{1}{\text{16}}\)

we have to solve for D

do you know how to add fractions?

Answer 35

I mean, I learned about that, but it was in like 6th grade so I pretty much forgot.

Answer 36

so to add fractions, you need to have the same denominator

so if you multiply the first fraction by 2 on the top and bottom, what do you get?

Answer 37

i suggest multiplying 1 by 2

Answer 38

Thats 2 ;-;

Answer 39

yes, so what's 2 times D

Answer 40

2D? This is so confusing

Answer 41

so, 2/2D

Answer 42

now remember

\(\dfrac{x}{z} + \dfrac{y}{z} = \dfrac{x+y}{z}\)

so for our question we have

\( \dfrac{2}{\text{2D}} + \dfrac{1}{\text{2D}} = \dfrac{1}{\text{16}}\)

Can you add the fraction?

Answer 43

i recommend adding 2 to 1