Let s(t) = amount, in kg of salt at time t.
ds/dt= (rate of salt into tank) − (rate of salt out of tank)
dtds=100−40010s=40040000−10s
40000−10sds=400dt
∫40000−10sds=∫400dt
−101ln(40000−10s)=400t+C
ln(40000−10s)=−40t+C2
40000−10s=C3e−t/40
s=−10C3e−t/40−40000
S(0)=0
0=−10C3e−0/40−40000
C3=40000
s=−1040000e−t/40−40000=−4000(e−t/40−1)
If s=90
90=−4000(e−t/40−1)
e−t/40=90/(−4000)+1=0.9775
−40t=ln(0.9775)=−0.0228
t=0.91 min.
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