## anonymous one year ago Simultaneous Equation problem

1. anonymous

Two taps A and B fill a swimming pool together in two hours. Alone, it takes tap A three haours less than B to fill the same pool. How many hours does it take each tap to fill the pool separately?

Is it 3 and 6 hours .

3. anonymous

4. anonymous

this is an equation right

5. anonymous

Yes

6. anonymous

ok this is what i found ....... http://www.algebra.com/algebra/homework/equations/Equations.faq.question.616566.html

7. anonymous

this should give you a better understanding then what we gave you .. this question does not seem complete

8. anonymous

It doesn't :(

9. anonymous

what do you need

10. anonymous

I want to know how one would solve this question

11. anonymous

Will i do or you will do @HWBUSTER00

12. anonymous

well i tired to help @Catch.me can you do it

13. anonymous

OK the main concept of these problems is to convert words to equation, so just get sentences and write the corresponding equation Two taps A and B fill a swimming pool together in two hours. means $A + B = 2$ Alone, it takes tap A three hours less than B to fill the same pool. $A = B - 3$ now you have 2 equations 2 unknowns substitute in the first equation using last equation

14. anonymous

So, $$A=2-B$$ and $$A=B-3$$? Therefore $2-B=B-3$$-B=B-5$$-2B=-5$$B=\dfrac{5}{2}$

15. anonymous

$A=2-b$$A=-\dfrac{1}{2}$Which is impossible :(

16. anonymous

@Catch.me?

17. anonymous

OK first equation was wrong A = x to fill 1 liter B = y to fill 1 liter so in 2 hours x : 1 2 : ?? A will fill 2/x B will fill 2/y so 2/a + 2/b = 2

18. anonymous

no equal 2 but 1

19. anonymous

hole tank

20. anonymous

I'm really confused now. Can you elaborate @Catch.me?

21. anonymous

I made a mistake in understanding the first sentence Two taps A and B fill a swimming pool together in two hours means that the amount of A filling in 2 hours + the amount of B filling in 2 hours will make the tank full lets say A fills tank in 7 hours so in 2 hours it fills 2/7 of that tank. so (2/a) + (2/b) = 1

22. anonymous

ok

23. anonymous

now you have 2 equations 2 unknowns solve them $\frac{ 4b-6 }{ b ^{2}-3b }= 1$ of course when b = 3 is neglected. so $B ^{2}-7B+6=0$ B=6 or 1 is neglected

24. anonymous

@Ahsome ?

25. anonymous

How did you go from (2/a)+(2/b)=1 to that @Catch.me?

26. anonymous

put a = b-3 and make multiply them

27. ParthKohli

OK so let's say that one tap takes $$x$$ hours and the other one takes $$x+3$$. Then the fraction of work they do in one hour is given by $$1/x + 1/(x+3)$$ but since it takes two hours for them to do the work, it is also given by $$1/2$$$\Rightarrow \dfrac{1}{x} + \dfrac{1}{x+3} = \dfrac{1}{2}$$\Rightarrow x = 3$

28. anonymous

common denominator

29. anonymous

Ahh, I see. So x would be the slower tap, right?

30. anonymous

@Ahsome do you understand this question now?

31. anonymous

No, I still don't :(

32. anonymous

B fills 1 pool per x hours ----> rate of B filling a pool = 1/x A = B - 3 hours, so A fills 1 pool per x - 3 hours ----> rate of A filling a pool = 1/(x - 3) now we know the rates of each so we have this, both taps fill 1 pool in 2 hours, 2 hours * (rate of B) + 2 hours * (rate of A) = 1 pool filled 2* (1/x) + 2 * (1/(x-3)) = 1

33. anonymous

when you solve that for x you get 2 answers for x one of these will not make sense if you plug into this equation A = B - 3, will give a negative result, and we know this makes no sense because the number of hours it takes to fill the pool cannot be negative, so the answer that makes sense is 6 hours for B, then you just subtract 3 from that to get 3 hours for A

34. anonymous

the method ParthKholi used is the same thing except he used B = A + 3 instead of A = B -3 , if you divide both sides of this equation by 2 2* (1/x) + 2 * (1/(x-3)) = 1 you will get a similar equation to what he had

35. anonymous

i hope that helps

36. anonymous

37. anonymous

Thank you so much @billj5. I'm kinda busy now, but I will definately look at this afterwards :)

38. anonymous

yw