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Math Help - please help

  1. #1
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    please help

    tab B alone takes 2 minutes longer than tap A to fill one tub. Working together, they can fill the tub 4 times in 5 minutes. How long does it take tap A (alone) to fill one tub? ((to 2 decimal places if necessary))
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  2. #2
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    Let a = tap A time.

    Then tap b is A+2

    They fill the tub 4 times in 5 minutes.

    \frac{1}{a}+\frac{1}{a+2}=\frac{4}{5}

    Solve for a and b will be two minutes more.
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  3. #3
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    could you define all the variables and where the numbers and equations come from... i just want to really understand the problem


    like for example why is it 1/a? etc
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  4. #4
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    Quote Originally Posted by finch41 View Post
    could you define all the variables and where the numbers and equations come from... i just want to really understand the problem


    like for example why is it 1/a? etc
    Hi, finch41. As galactus explained, a is the amount of time it takes tap A to fill 1 tub. That means tap A fills 1 tub per a minutes, so the rate is \frac1a\text{ tubs/min}. Similarly, tap B takes a + 2 minutes (2 minutes more than tap A) to fill the tub, so it has a fill rate of 1 tub per a + 2 minutes, or \frac1{a + 2}\text{ tubs/min}. But, when both taps are on, they fill 4 tubs every 5 minutes, so we have a rate of \frac45\text{ tubs/min}. This gives us the equation,

    \text{rate of tap A}\;+\;\text{rate of tap B}\;=\;\text{combined rate}\Rightarrow\frac1a + \frac1{a + 2} = \frac45

    Solve for a.
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