FLVSKidd
  • FLVSKidd
Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her own.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
FLVSKidd
  • FLVSKidd
Okay I think I know the answer, I just know that my teacher will not accept the answer without the formula and steps.
FLVSKidd
  • FLVSKidd
which is confusing me
anonymous
  • anonymous
so u just don't know the formula

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

FLVSKidd
  • FLVSKidd
you could say that
phi
  • phi
I would use the formula rate * time = work done in this case, the work done is 1 room so rate_carl * t1 = 1 (room) and rate_jen * t2 = 1 where t1 is the time it takes carl and t2 the time for jen carl is 3 hours faster than jen which means t1 is 3 hours shorter than t2 in other words t1= t2-3
FLVSKidd
  • FLVSKidd
Here is an example similar to the question. Maybe this will ring a bell.
FLVSKidd
  • FLVSKidd
1 Attachment
FLVSKidd
  • FLVSKidd
i included the steps
phi
  • phi
They are using some "short cut" formula that is not easy to follow, but does work. If we ignore why it works (which is not something I usually do), and just use it, we write \[ \frac{1}{t_1}+ \frac{1}{t_2}= \frac{1}{t_{total}}\] where t1 is the time it takes for one person to do the job (working alone) t2 the amount of time for the other person to do the job working alone and t_total is the amount of time to do the job when working together
FLVSKidd
  • FLVSKidd
okay so I would plug 3 and 2 as the first two denominators?
phi
  • phi
They say If they work together, they can complete the job in 2 hours that means t_total is 2 we can put that into the formula \[ \frac{1}{t_1}+ \frac{1}{t_2}= \frac{1}{t_{total}} \\ \frac{1}{t_1}+ \frac{1}{t_2}= \frac{1}{2}\]
phi
  • phi
they want to find Jen's time. that is obviously unknown, so let's assume she is t1, but we will use "x" for unknown. Put x in for t1 \[ \frac{1}{x}+ \frac{1}{t_2}= \frac{1}{2} \]
phi
  • phi
Now you have to figure out what this means Carl can paint a room 3 hours faster than Jennifer can what is the time t2 (Carl's time) ? we are using x for jen's time, so we can say t2 (carl's time) is 3 hours less than x
phi
  • phi
do you know how to write 3 less than x in algebra?
FLVSKidd
  • FLVSKidd
3>x ?
FLVSKidd
  • FLVSKidd
3
phi
  • phi
good guess, but that is not what they mean what is 3 less than 10 ?
FLVSKidd
  • FLVSKidd
7
phi
  • phi
and 3 less than 8 ?
FLVSKidd
  • FLVSKidd
5
phi
  • phi
notice 3 less than 10 you figured out by doing 10-3 and for 3 less than 8 you did 8-3 what is 3 less than x?
FLVSKidd
  • FLVSKidd
-3x ?
phi
  • phi
use the same idea as when you do 3 less than 5 you write 5 then a - sign then 3 5-3 =2 3 less than 5 is 2 now do 3 less than x
FLVSKidd
  • FLVSKidd
x-3
phi
  • phi
yes. it is a way of "thinking" that is useful. so if jen takes x hours, carl takes x-3 hours (3 hours less than jen's x)
phi
  • phi
replace t2 with x-3 in the equation \[ \frac{1}{x}+ \frac{1}{x-3}= \frac{1}{2} \]
phi
  • phi
do you have to solve this ? you get a quadratic equation that you have to factor.
FLVSKidd
  • FLVSKidd
ok i understand so I solve x+x-3=2
phi
  • phi
no, it's messier. one way to proceed is to multiply both sides (and all terms) by x(x-3) can you do that?
FLVSKidd
  • FLVSKidd
i think so let me try
FLVSKidd
  • FLVSKidd
sorry for being slow. if I was to multiply 2 by x(x-3) would i plug in 2 for the xs
FLVSKidd
  • FLVSKidd
sorry i dont know how to multiply each term
phi
  • phi
you write x(x-3) next to each term
phi
  • phi
notice you can simplify the first term because x divided by x "cancels" and in the 2nd term (x-3)/(x-3) also cancels.
FLVSKidd
  • FLVSKidd
yes I see that, would the same apply for (x-3) over (x-3)
phi
  • phi
\[ \frac{x(x-3)}{x}+ \frac{x(x-3)}{(x-3)}= \frac{x(x-3)}{2} \] or after simplifying \[ (x-3) + x = \frac{x(x-3)}{2} \]
FLVSKidd
  • FLVSKidd
gotcha
phi
  • phi
can you simplify the left side x-3+x
FLVSKidd
  • FLVSKidd
2x-3?
phi
  • phi
yes, so you have \[ 2x-3 = \frac{x(x-3)}{2} \] if we multiply both sides by 2 we can get rid of the fraction on the right side \[ 2(2x-3) = \cancel{2}\cdot \frac{x(x-3)}{\cancel{2}} \] \[ 2(2x-3)= x(x-3) \] I would "distribute the 2" on the left side can you do that ?
FLVSKidd
  • FLVSKidd
4x-12
phi
  • phi
ok except 2*3 is 6 (not 12)
FLVSKidd
  • FLVSKidd
i feel so stupid sorry
phi
  • phi
\[ 4x -6 = x(x-3) \] it's easy to make simple mistakes. you have to go slower and more carefully (remember, you have to learn math and it's painful) now distribute the x on the right side
FLVSKidd
  • FLVSKidd
4x-6 = x^2 -3x
phi
  • phi
now "move" the terms on the left side to the right side: add -4x+6 to both sides
FLVSKidd
  • FLVSKidd
x^2 -7x +6 ?
phi
  • phi
ok, but it's an equation \[ 0= x^2 -7x +6 \] or \[ x^2 -7x +6 =0 \]
FLVSKidd
  • FLVSKidd
okay so do i factor?
phi
  • phi
yes , and it does factor
FLVSKidd
  • FLVSKidd
(x-6)(x-1)
phi
  • phi
yes but you should write the whole equation (x-6)(x-1)= 0 you get x=6 or x=1 x is the time it takes Jen to do the job. carl is 3 hours faster. So , even though the math has a solution x=1 (as a possibility) we can rule it out, because carl's time can't be 1-3 = -2 hours that leaves jen's time as 6 hours and carl's time as 3 hours
FLVSKidd
  • FLVSKidd
so that is the solution?
phi
  • phi
yes
FLVSKidd
  • FLVSKidd
Okay thank you very much for dealing with me and helping.

Looking for something else?

Not the answer you are looking for? Search for more explanations.