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    Can somebody please explain how to do this question, i kinda can get to an answer but it isnt the one given in the book

    a boy is eating a 250g hamburger. when he has eaten mass m grams his rate of consumption is 100 - m^2/900 grams per minute. how long does he take to finish his meal?

    Please help :eek:
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    dm/dt = 100 - m²/900
    1/(100-m²/900) dm/dt = 1

    get the partial fractions:

    1/(100-m²/900) == 1/[(10-m/30)(10+m/30)] == A/(10-m/30) + B/(10+m/30)

    10A + 10B = 1, mA - mB = 0

    => A = B = 1/20

    => [1/(200-2m/3) + 1/(200+2m/3)] dm/dt = 1

    integrate wrt t:

    -3/2 ln|200-2m/3| + 3/2 ln|200+2m/3| = t + c

    => 3/2 ln|A(200+2m/3)/(200-2m/3)| = t

    init conditions: [email protected]=0 => A = 1

    m=250: t = 3/2 ln2 minutes ~= 1 minute, 2 seconds
 
 
 

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