My math teacher NEVER taught us this!!!?

Question

tell me how to set this up and solve please...just dont gimme the answer...


here is the problem and the section it is from is called applications of rational expressions if it helps

Working together lauren and david can do a job in 4 hours. Working alone, it would take david twice as long as lauren to do the job. How long would it take lauren to do the job alone.


please help me!!!

Answer 1

Lauren and David do it in 4 hours
L + D = 4

David takes TWICE as long as Lauren
D = 2L

SUBSTITUTE 2L for the D in the fist equation
L + D = 4
L + (2L) = 4
........3L..= ....4
........./3........./3
..........L...=...4/3 OR 1-1/3
..........L..= 1-1/3 of 60 minutes (hr)
..........L..= 80 minutes

D= ..2L
D=2 X (4/3)
D=8/3
D=2-2/3
D= 2-2/3 of 60 mins
D= 160 minutes

Answer 2

Nice problem. I'm good at math, but English is not my native language (I'm italian) so please forgive me if my answer is not clear.

Let X be the total amount of job to be done and let D and L be the amount of job per hour that David and Lauren can do.

Hence X=D*T+L*T=(D+L)*T where T=4 hours is the time they need to complete the job working together. We know that working alone it would take David twice as long as Lauren to dso the job. That is: X=D*(2*T')=L*(T'). This means that L=2*D (and D=L/2).

We are almost done: since L=2*D then X = (D+2*D)T = (3*D)*T = (3/2)*L*T = L*[(3/2)*T]. Hence it would take Lauren (3/2)*T=6 hours to complete the job.

The solution should be correct, I only hope I explained everything well.

Answer 3

The key is to figure out what part of the job each
can do in 1 hour.
Let x be the number of hours it takes Lauren to
do the job.
Then in 1 hour she can do 1/x of the work.
Since it takes David twice as long to do the job,
he can do 1/2x of the job in 1 hour.
Together it takes them 4 hours to do the job
so they can do 1/4 of it in 1 hour if they work
together.
So
1/x + 1/2x = 1/4.
Combining the fractions,
3/2x = 1/4
2x = 12
x = 6.
It would take Lauren 6 hours and David 12 hours
to do the job alone.
Hope that helps!!

Answer 4

Let L be lauren, and D be david. L+ D=4 hours
D =2L
then do the substitution method, which you plug in the D=2L into the equation, L+D=4, where it says D.
Plug: L+2L=4 . L+2L=3L,so 3L=4, then divid both side by 3, which equal to 4/3. If you don't get it read it over again. Good luck!

Answer 5

Going on of what Kittenpie went of of. Since D+L=4 and D=2L, you replace the D on the first equation with 2L so you get, 2L+L=4. You combine like terms, 3L=4, then divide by 3, L=4/3, so 4/3 hour or 1hr. 20 min.

But then that doesn't make sense, so sorry.

Answer 6

OK, so Lauren's time + David's time is 4 hours.
L + D = 4
If they both do the same job, David takes twice as long as Lauren. (David's time is the same as 2 times Lauren's time.)
D = 2L

Can you solve the problem now?

Answer 7

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Answer 8

that doesn't make sense- did you copy it down right?