Question

how do i set up the equation for this?

Jordan is a manager of a car dealership. He has 3 professional car washers to clean the entire lot of cars, Jennifer, Arianna, and Matthew. Jennifer can wash all the cars in 14 hours. Arianna can wash all the cars in 11 hours. Matthew is new to the car dealership, so no one knows how long it will take him.

Jordan assigns all of them to wash the cars together. Explain to Jordan how this task can tell him how long it would take Matthew to complete the task if he worked by himself. Use complete sentences.

Answer 1

@Hannah_Waller

Answer 2

give me a medal for helping you last time and ill tell you

Answer 3

OK where do you think you start?

Answer 4

@Hannah_Waller I know the equation up to this point
1/14 + 1/11 + 1/M = 1/t

Answer 5

@bigsexy75 nice way to help someone out.

Answer 6

then you end up getting \[25 \over 154\]

Answer 7

So you know this,


Has a total of 3 car washers

J- Can wash cars in 14 hours

A- Can wash cars in 11 hours

M- ?

Answer 8

so im not sure how you got decimas... im confuseed haha

Answer 9

decimals?

Answer 10

haha i meant fractions

Answer 11

Their not fractions, more like proportions

Answer 12

that's just how you set up the problem

Answer 13

oh ok sorry i dont completly get it... :(

Answer 14

@phi could you please help understand this?

Answer 15

I guess you have to solve for M

Answer 16

Yes, but I don't know how to get it that

Answer 17

one technique is to "clear the denominators"
by multiply the equation by 11*14*t (all terms both sides)

Answer 18

wait, what do you mean? sorry, this is really confusing for me

Answer 19

like this
\[ 14\cdot 11\cdot t \left( \frac{1}{11} +\frac{1}{14} +\frac{1}{m} \right) = 14\cdot 11\cdot t \cdot \frac{1}{t} \]

Answer 20

ohh okay, so once i've got that, what do i do?

Answer 21

I have not done this, so you can work along and see how it goes.

Answer 22

I've never done it this way. I usually just cross multiply and then divide to get my answer, but this one includes matthew so it's confusing

Answer 23

yes, 3 things is more complicated. but distribute the 11*14*t
what do you get ?

Answer 24

if you don't like this way, we can do it using fractions
starting with
\[ \frac{1}{11} +\frac{1}{14} +\frac{1}{m} = \frac{1}{t} \]
add the first two numbers (which you did up above) to get 25/154
\[ \frac{25}{154} +\frac{1}{m} = \frac{1}{t} \]

subtract 25/154 from both sides
\[ \frac{25}{154} - \frac{25}{154} +\frac{1}{m} = \frac{1}{t} -\frac{25}{154}\\
\frac{1}{m} = \frac{1}{t} -\frac{25}{154}
\]

Answer 25

now combine the left side using a common denominator of 154 t
\[ \frac{1}{m} = \frac{1}{t} -\frac{25}{154} \\
\frac{1}{m} = \frac{1}{t}\cdot \frac{154}{154} -\frac{25}{154}\cdot \frac{t}{t} \\
\frac{1}{m} = \frac{154-25t}{154t}
\]

Answer 26

are you following?

Answer 27

*now combine the *right* side using a common denominator of 154 t

Answer 28

that's where i'm confused, what exactly am i combining?

Answer 29

\[ \frac{1}{t}- \frac{25}{154} \]

Answer 30

do you see you want a common denominator of 154t ?

Answer 31

ohhh okay, sorry i wasn't looking at the right thing, yes i see that

Answer 32

so multiply the first fraction by 154/154
and the second fraction by t/t

Answer 33

yes, got that

Answer 34

did you get all the steps so far?

Answer 35

Yes I do, now for the last part do we have to multiply 154t on both sides?

Answer 36

we now have
\[
\frac{1}{m} = \frac{154-25t}{154t} \]
the simplest thing to do is "flip" (i.e. invert) both sides
\[ m = \frac{154t}{154-25t} \]

Answer 37

okay, i don't know what to do from there

Answer 38

Explain to Jordan how this task can tell him how long it would take Matthew to complete the task alone

Answer 39

you tell Jordan to time how long all 3 take to do the job. That will be "t" in your equation
put in that number for "t", and solve (figure out) how fast M can do the job by himself.

Answer 40

For example, if it takes all 3 people 3 hours to do the job, then
M= 3*154/(154-3*25) = 5.85 hours or about 5 hours 51 minutes

Answer 41

so whatever number i get i plug it in for t and that is my answer

Answer 42

Yes. The question is asking how to figure out how long M takes working alone.
You explain how by saying,
time how long all 3 take to do the job.
Use that time in the equation to find M

Answer 43

You can't find M unless you know how long it takes the 3 to do the job, and we don't know that.

Answer 44

oh okay, got it. Thank you so much for your help and patience, i appreciate it!! :)

Answer 45

so you get it that we don't know "t"? right? but if we did, we know how to find M.

Answer 46

yes, i got that