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25 October, 12:57

Water flows into a tank according to the rate F (t) = (6+t) / (1+t), and at the same time empties out at the rate E (t) = ln (t+2) / (t+1), with both F (t) and E (t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t = 10 minutes.

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  1. 25 October, 15:43
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    F (t) = 1.5 gallon / min

    E (t) = 5.5 gallon/min

    Step-by-step explanation:

    The rate at which water flows into the tank = F (t)

    The rate at which water is emptied from the tank = E (t)

    F (t) = (6+t) / (1+t)

    E (t) = ln (t+2) / (t+1)

    When t = 10 mins

    F (t) = (6 + 10) / (1+10)

    = 16/11

    F (t) = 1.5 gallon / min

    E (t) = ln (10 + 2) (10+1)

    = ln (12) (20)

    = ln (240)

    E (t) = 5.5 gallon/min
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