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Thread: Algabaric time messaure...

  1. #1
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    Algabaric time messaure...

    To a bath there are two taps:
    one - fill the bath half an hour.
    the second - fill the bath third of the hour.
    The taps open together.

    What the time the bath will be filled about?
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  2. #2
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    Re: Algabaric time messaure...

    Let's convert to minutes. Tap 1 does the job in 30 minutes while tap 2 does it in 20 minutes.

    So, together, it will take $\dfrac{30\cdot 20}{30 + 20} = \dfrac{600}{50} = 12$ minutes.
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    Re: Algabaric time messaure...

    Thanks.
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    Re: Algabaric time messaure...

    x = time in hours both taps work together

    rate 1 = how many baths tap 1 fills in one hour

    rate 2 = how many baths tap 2 fills in one hour

    1 = the whole job

    x(rate 1 + rate 2) = 1

    x(2 + 3) = 1

    5x = 1

    x = 1/5

    1/5 hour

    or

    12 minutes
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  5. #5
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    Re: Algabaric time messaure...

    @1/20mpm...................1....................>20mi n
    @1/30mpm...................1....................>30mi n
    @(1/20+1/30)mpm........1....................>12min : 1/(1/20+1/30)
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  6. #6
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    Re: Algabaric time messaure...

    Or: "one - fill the bath half an hour" fills the bath at the rate of 2 baths per hour.

    "the second - fill the bath third of the hour" fills the bath at the rate of 3 baths per hour.

    Together, they fill the bath at the rate of 2+ 3= 5 baths per hour.

    That is a rate of 1/5 hour per bath or 60/5= 12 minutes to fill one bath.
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  7. #7
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    Re: Algabaric time messaure...

    Think I'll take a shower!
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  8. #8
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    Re: Algabaric time messaure...

    Quote Originally Posted by greg1313 View Post
    x = time in hours both taps work together

    rate 1 = how many baths tap 1 fills in one hour

    rate 2 = how many baths tap 2 fills in one hour

    1 = the whole job

    *** x(rate 1 + rate 2) = 1
    How I know the formula (***)?
    Why this formula is true?
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    Re: Algabaric time messaure...

    Quote Originally Posted by policer View Post
    How I know the formula (***)?
    Why this formula is true?
    Are you familiar with

    time*rate = distance (quantity)?
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  10. #10
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    Re: Algabaric time messaure...

    O.K.
    Why the isn't (1/2+1/3) instead 5...?
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  11. #11
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    Re: Algabaric time messaure...

    Quote Originally Posted by policer View Post
    O.K.
    Why the isn't (1/2+1/3) instead 5...?
    Tap 1 fills the bath in half an hour, or its rate is two full baths per hour.

    Tap 2 fills the bath in a third of an hour, or its rate is three full baths per
    hour.
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  12. #12
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    Re: Algabaric time messaure...

    Again, why isn't it 1/2 + 1/3...?
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  13. #13
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    Re: Algabaric time messaure...

    Quote Originally Posted by policer View Post
    Again, why isn't it 1/2 + 1/3...?
    What do you get if you add those? 1/2 hour to fill the bath+ 1/3 hour to fill the bath= 3/6+ 2/6= 5/6 hour per bath, almost an hour. Does it make sense that using both taps it would take longer to fill the bath than only one?

    A rate is 'progress (distance, filling a bath, doing a job, whatever) per hour'. You need to invert to get 2 and 3 baths per hour.
    Last edited by HallsofIvy; Feb 13th 2018 at 05:54 AM.
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  14. #14
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    Re: Algabaric time messaure...

    Quote Originally Posted by policer View Post
    Again, why isn't it 1/2 + 1/3...?
    1/2 + 1/3 = 3/6 + 2/6 = 5/6: bath NOT full!
    If you're still not satisfied, go take a shower!!
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