## anonymous 4 years ago 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!!

1. anonymous

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

2. anonymous

|dw:1330229793561:dw|

3. anonymous

would you move everything with an a on one side

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.

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

6. anonymous

huh?? alll ternmss

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?

The equation is not valid as denominator results in 0

9. anonymous

yes i did

10. anonymous

soo no solution

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

12. anonymous

|dw:1330230347158:dw|

No solition.

14. anonymous

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

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

16. anonymous

ohh yeaa

17. anonymous

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

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

19. anonymous

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

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

22. anonymous

i see it next problem

I will leave the proof up to you.

24. anonymous

|dw:1330230943000:dw|

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

26. anonymous

yess

27. anonymous

we would mulktiply by d

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

29. anonymous

its 2-d

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|

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

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

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

|dw:1328676821005:dw|

35. 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?

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

37. anonymous

so its one solution

Yes

Can not divide by 0.

40. anonymous

next problem and last

41. 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?

42. anonymous

hello??

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.

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

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

46. anonymous

thnk u sooooo much youve really helped meee

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)

Good night and good luck in your studies.

49. anonymous

thnks

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