Sand pours out of bag at a rate of r(t) = 100 − 3t mL/min until the bag runs out of sand at t = 20 min. How much sand was originally in the bag?

Question

Im not sure how I would solve this problem, any help would be appreciated!

Answer 1

The volume of sand in the bag is equal to the integral of the dV/dt of the bag.or

dV = rdt

integral from V₀ to 0 = integral from 0 to 20 min of -(100-3t)dt (I made the rate negative because Volume of sand is leaving the bag:

-V₀ = -(100t - 3t²/2) from 0 to 20

V₀ = 100(20) - 3/2 *20² = 1400 ml