Painting in Series and Parallel

Let's call the amount of work Bob does in an hour $B$ and the amount of work Alice does in an hour $A$ . Then $A=2B$

In the first case, they have two brushes, work for 16 hours, and get the job done.

The total amount of work they get done is $16A+16B=32B+16B=48B$

In the second case they have only one brush, so only one of them works at a time, each doing half of the job, that is $24B$ .

Bob does his $24B$ in $24$ hours.

Alice does the same $24B$ in half the time, that is $12$ hours.

The total time is the sum of the two, $24+12=\boxed{36}$ hours.

$A = 2B$

$B = \dfrac{A}{2}$

$H = A+B$

---

Alice

$H = A + \dfrac{A}{2} = \dfrac{2A}{2}+\dfrac{A}{2} = \dfrac{3A}{2}$

$\dfrac{2}{3}H = A$

Alice can paint $\dfrac{2}{3}$ of a House in 8 hours.

$\dfrac{3}{2} \times 8 = \boxed{12}$

---

Bob

$H = 2B + B = 3B$

$\dfrac{1}{3}H = B$

Bob can paint $\dfrac{1}{3}$ of a House in 8 hours.

$3 \times 8 = \boxed{24}$

---

$\boxed{12} + \boxed{24}$ = $\large\boxed{36}$