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Math Help - application of integration to rate of flow

  1. #1
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    Post application of integration to rate of flow

    Wine is leaking from a barrel at the rate of r(t) = 10 − 0.1t litres per minute.

    i) If the barrel is empty after 100 minutes, how much wine did the barrel initially
    hold?

    ii) How much wine is in the barrel after 60 minutes?

    I have never worked with flow before so just wanted to make sure what I was doing was correct.

    I took the integral of the flow. Then put t = 100 in to find the c value. I found the value to be negative 500 so I think I did something wrong.

    Am I going about this the right way?
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  2. #2
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    Quote Originally Posted by stabza View Post
    Wine is leaking from a barrel at the rate of r(t) = 10 − 0.1t litres per minute.

    i) If the barrel is empty after 100 minutes, how much wine did the barrel initially
    hold?

    ii) How much wine is in the barrel after 60 minutes?

    I have never worked with flow before so just wanted to make sure what I was doing was correct.

    I took the integral of the flow. Then put t = 100 in to find the c value. I found the value to be negative 500 so I think I did something wrong.

    Am I going about this the right way?
    amount leaked in 100 minutes ...

    \displaystyle \int_0^{100} r(t) \, dt

    ... should tell you how much was in the tank to start.


    amount left at 60 minutes = initial amount - \displaystyle \int_0^{60} r(t) \, dt
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  3. #3
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    get it now
    thanks
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