The masses of ice and water in a sealed cooler satisfy for all

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The masses of ice

m_i(t)

and water

m_w(t)

in a sealed cooler satisfy

m_i(t)+m_w(t)=5\text{ kg}

for all

t

. Explain why

\displaystyle \frac{dm_i}{dt} = -\frac{dm_w}{dt}