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# Differential equation question watch

1. 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
2. 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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