a/a+4=3-4
marian can weed a garden in 3 hrs. robinm can weed the same garden in 4 hrs. how longh will the weeding take them if they work together?
3/m-1=2m/m+4- solve this equation check solution if there is no solution put no solution
Help Please!!

- anonymous

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- anonymous

a/a+4=3-4/a+4

- anonymous

|dw:1330229793561:dw|

- anonymous

would you move everything with an a on one side

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## More answers

- radar

The weeding problem is solved by just taking the product divided by the sum
(3 X 4)/7=12/7 hr or 1 5/7 hour.

- radar

Multiply all terms by (a+4) getting
a = 3(a+4)-4
a = 3a +12 -4
-2a=8
a=-4

- anonymous

huh?? alll ternmss

- radar

To check (-4)/(-4+4) can't go any further as division by 0 is not permitted. Let me check my work. Are you sure you have it copied correctly?

- radar

The equation is not valid as denominator results in 0

- anonymous

yes i did

- anonymous

soo no solution

- radar

|dw:1328675059499:dw||dw:1328675072118:dw|
The equation has 3 terms.

- anonymous

|dw:1330230347158:dw|

- radar

No solition.

- anonymous

i get it now next problem do we multiply by m?

- radar

dessyk, have you ever heard of cross multiplying? We could do that.

- anonymous

ohh yeaa

- anonymous

3m+12=2m^2-2m

- radar

3(m+4)=2m(m-1)
3m + 12 =2m^2 -2m
Yes you got now consolidate and simplify
\[2m ^{2}-5m-12=0\]

- anonymous

then the quadratic equation?

- radar

Factor getting (m-4)(2m+3)
m=4
m=-3/2
those are the two solutions.

- radar

Yes it is a quadratic, but a easily factored one lol

- anonymous

i see it next problem

- radar

I will leave the proof up to you.

- anonymous

|dw:1330230943000:dw|

- radar

Is the last term d+6 over d^2-4?

- anonymous

yess

- anonymous

we would mulktiply by d

- radar

And are you sure that the denominator of the 2nd term is 2-d or is it d-2 ??

- anonymous

its 2-d

- radar

O.K First I am going to change the 2nd terms appearance, but not its value by multiplying it by -1 and again by-1 (which is 1) so the equation will now look like this:|dw:1328676105960:dw|

- radar

Note that (d^2-4) is (d+2)(d-2)
Now multiply all terms by (d^2-4) getting
\[d ^{2}-2d +2d+4 = d\]No tricks here everything legal lol

- radar

Simply: \[d ^{2}-2d+2d+4=d+6 \]ooops I made a mistake I dropped of that 6 so it is now.

- radar

\[d ^{2}-d-2=0\]can be factored (d-2)(d+1)
d=2
d=-1
Proof left up to you.

- radar

|dw:1328676821005:dw|

- anonymous

two pipes fill a storage tank in 9 hrs. the larger pipe fills the tank 3 times as fast as the smaller one . How long would it take the larger pipe to fill the tank alone?

- radar

d=2 is not a valid solution as it would result in zero in the second term,so d=-1

- anonymous

so its one solution

- radar

Yes

- radar

Can not divide by 0.

- anonymous

next problem and last

- anonymous

- anonymous

hello??

- radar

First you know the larger pipe will fill it quicker than the smaller one.
let x time to fill with larger pipe
then 3x is the time to fill with smaller pipe.
Use product over sum to solve this type problem especially when you only have two things working.
3x * x =3x^2
3x + x =4x
product over sum is:\[3x ^{2}\over4x\] and this equals 9 (given) solve by cross multiplying: 36x=3x^2 or \[3x ^{2}-36x=0\]factoring getting: 3x(x-12)=0
x=12 large pipe will fill it in 12 hours, small pipe will take 36 hours,together 9 hours.

- radar

Thats all for me tonight. Be sure and double check answers by proofing.

- radar

That way if I goofed you will be able to correct my mistake.

- anonymous

thnk u sooooo much youve really helped meee

- radar

ur welcome, I was just looking at that last one and it would be simpler to just reduce that
3x^2/4x to 3x/4 and set that to =9
3x/4 =9 getting 3x =36, x=12 (no quadratic that way lol)

- radar

Good night and good luck in your studies.

- anonymous

thnks

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