A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Ahsome

  • one year ago

Simultaneous Equation problem

  • This Question is Closed
  1. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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?

  2. Pawanyadav
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is it 3 and 6 hours .

  3. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    They haven't given answers @Pawanyadav. How did you solve it?

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is an equation right

  5. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  8. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It doesn't :(

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what do you need

  10. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I want to know how one would solve this question

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Will i do or you will do @HWBUSTER00

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, \(A=2-B\) and \(A=B-3\)? Therefore \[2-B=B-3\]\[-B=B-5\]\[-2B=-5\]\[B=\dfrac{5}{2}\]

  15. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  16. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Catch.me?

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no equal 2 but 1

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hole tank

  20. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  21. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Ahsome ?

  25. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    put a = b-3 and make multiply them

  27. ParthKohli
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    common denominator

  29. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Ahsome do you understand this question now?

  31. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, I still don't :(

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i hope that helps

  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i recommend watching some of these videos https://www.khanacademy.org/math/algebra/ratio-proportion-topic/advanced-ratios/v/another-take-on-the-rate-problem

  37. ahsome
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yw

  39. Pawanyadav
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The answer was right.

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.