Water In, Water Out, and Which Way the Level Goes

You'll learnto put the minus sign on a drain from the first line, to build a net rate as in minus out, and to keep both halves of a unit when the thing you differentiate is already a rate.

A tank has a pipe pouring water in and a drain letting water out. The pipe never slows down, and yet partway through the tank starts losing water. Eleven short steps; press Next for each one.

11 STEPS · 6 QUICK CHECKS · AN OUTFLOW IS NEGATIVE FROM THE START · NET = IN − OUT · A RATE OF A RATE STACKS A UNIT · v2

R(t) = 20 + 4t in · S(t) = 3t² out ⇒ dA/dt = R − S, zero at t = 10/3

Before you start

What you're looking at

A tank of water over five minutes, with a pipe pouring in and a drain letting out. The two bars beside it are those two rates, drawn to scale.

The question

The pipe never slows down, so why does the tank start losing water, and when?

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