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Math algebra problem

  1. Feb 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Two pumps of different sizes can empty an entire fuel tank in 4.8 hours. Used alone, the larger pump would empty the tank 4 hours less than would the smaller pump. If using only the smallest pump How long will it take to empty the tank?

    2. Relevant equations
    X = small pump
    X-4hours = bigger pump

    Y = 4.8 hours

    This is what I understand so far. I am not sure what to do next.

    3. The attempt at a solution
    4.8 = x - 4

    would that mean small pump needs 8.8 hours? am I doing this right?
     
    Last edited: Feb 14, 2015
  2. jcsd
  3. Feb 14, 2015 #2

    RUber

    User Avatar
    Homework Helper

    What is Y and where did 4.8 come from?

    You should have something like ## 1/X+1/Y=1/4##
    And
    ##Y=X-4##
     
  4. Feb 14, 2015 #3

    Mark44

    Staff: Mentor

    RUber asked about Y and where the 4.8 hours came from, a reasonable question, since the number 4.8 doesn't appear anywhere in the problem description above.

    A variable should represent an unknown quantity whose value you are trying to find.
    I can't think of any good reason why you should give this value the name Y.
     
  5. Feb 14, 2015 #4
    This is like a rate-time-distance problem. The rate that the smaller pump empties the tank is 1/X tanks per hour. The rate that the larger pump empties the tank is 1/(X-4) tanks per hour. How many tanks (of the same size) can the smaller pump empty in 4 hours? How many tanks (of the same size) can the larger pump empty in 4 hours? Together they empty 1 tank in 4 hours. Can you write an equation describing this?

    Chet
     
  6. Feb 14, 2015 #5
    My apology, I accidentally deleted the .8 while typing. I edited the OP. it takes 4.8 hours with both pump together.
     
  7. Feb 14, 2015 #6
    Both pump together can empty it in 4.8 hours. I edited the OP sorry for the confusion.
     
  8. Feb 14, 2015 #7
    OK. Substitute 4.8 hours for 4 hours. Are you able to answer my questions now?

    Chet
     
  9. Feb 14, 2015 #8
    I am sorry but I do not understand why it is 1/X, why is the 1 needed?
     
  10. Feb 14, 2015 #9
    If you drive your car 1 mile in X minutes, then your rate of travel is 1/X miles per minute (rate = distance/time). If you empty 1 tank in X hours, then your rate of emptying tanks is 1/X tanks per hour.

    Chet
     
  11. Feb 14, 2015 #10
    Oh so it should simply be 1/x + 1/x-4 = 1/Y
    1/x + 1/x-4 = 1/4.8

    Now I really have no idea how to factorize this and get the X value.

    The only thing I can thing off is doing something like this:

    1(4.8)(x-4) + 1(x*4.8) / (x)(x-4)(4.8) = 1(x)(x-4) / (x)(x-4)(4.8)

    4.8x - 19.2 + 4.8x ((x)(x-4)(4.8))= x^2 - 4x / (x)(x-4)(4.8)

    and I am stuck here.
     
  12. Feb 14, 2015 #11
    You seem to have the right idea, but you have to do the algebra correctly.

    Chet
     
  13. Feb 14, 2015 #12
    Thanks a lot for the help and the time :)

    @everyone who helped and took the time to read and support me with this, thank you every much :).
     
  14. Feb 14, 2015 #13
    Okay so I am getting x1= 1.6 and x2 = 12, the answer should be 12 right? since it cant really be under 4.
     
  15. Feb 15, 2015 #14

    RUber

    User Avatar
    Homework Helper

    The numbers check out.
     
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