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Algebraic word problem- basic

  1. Dec 6, 2012 #1
    I understand this is a basic problem. For some reason I just can't wrap my head around it. Any help is appreciated.

    1. The problem statement, all variables and given/known data
    Water flows through Pipe A five times faster than through Pipe B. When water flows through the both pipes a tank would be filled in 4 hours. How long will it take to fill a tank if only Pipe B opened?



    2. Relevant equations



    3. The attempt at a solution
    Pipe A: (5x)
    Pipe B: (x)
    Time: four hours.
     
  2. jcsd
  3. Dec 6, 2012 #2

    phinds

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    So if both pipes flow, it takes 4 hours but if only pipe B flows then it ALSO takes 4 hours ? Does that seem likely to you?
     
  4. Dec 6, 2012 #3
    I presume the problem means to say that the volume of water passing through pipe A is 5 times greater than the volume passing through pipe B. If water flows through both pipes, how many times the volume of pipe B is flowing?
     
  5. Dec 6, 2012 #4
    Skeptic2 is right as far as interpreting the problem goes. Can anyone help me out?!
    Thanks.
     
  6. Dec 6, 2012 #5

    haruspex

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    You've written that water flows through A at rate 5x and through B at rate x. If both flowing, what's the total rate? If that takes 4 hours to fill, how big is the tank?
     
  7. Dec 6, 2012 #6
    Your "attempt at a solution" says that pipe B delivers an amount x of water in a specified time to the tank. And pipe A delivers an amount 5x to the tank in the same time.

    So how much do A and B deliver to the tank together (again, in the time we're using in these measurements)?
     
  8. Dec 6, 2012 #7

    SammyS

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    Answering Skeptic2's question at the end of his post should help you out.
     
  9. Dec 6, 2012 #8
    That's all the info that the problem gives.
    Like I said I'm sure this is really easy for most people but I just can't wrap my head around it.
     
  10. Dec 6, 2012 #9
    So if A can deliver 5 liters per second and B can deliver 1 liter per second, how many liters per second can A plus B deliver?
     
  11. Dec 6, 2012 #10
    6 liters per second
    So would it take six hours to fill the tank if only B were open? Or 5?
     
  12. Dec 6, 2012 #11

    phinds

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    You are not even close.

    I've found that the best way to solve these "vague" problems is to make them specific and to do so in a way that simplifies the calculations.

    Since you have a speed X and a speed 5X, ASSUME that your tank contains 6 liters (that the one plus the 5). From this you can deduce a value for X. Then you can go back and see what effect 1X would have, given that you know what effect 6X has.
     
  13. Dec 6, 2012 #12
    So if at 6 liters per second it takes 4 hours to fill the tank, how big is the tank?

    Ans.: 4 hr x 3600 sec/hr x 6 liters / sec. = 86400 liters.

    How many hours would it take to fill the tank at 1 liter/sec?
     
    Last edited: Dec 6, 2012
  14. Dec 15, 2012 #13
    Thanks everybody for all your help. I was able to figure it out with your help.

    I got 24 hours as the final answer and the professor said it was correct.
    Thanks again!
     
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