AMC12 2008 12B, Problem 10

Bricklayer Brenda would take $9$ hours to build a chimney alone, and bricklayer Brandon would take $10$ hours to build it alone. When they work together they talk a lot, and their combined output is decreased by $10$ bricks per hour. Working together, they build the chimney in $5$ hours. How many bricks are in the chimney?

Solution: Let $h$ be the number of bricks in the chimney. Without talking, Brenda and Brandon lay $\frac{h}{9}$ and $\frac{h}{10}$ bricks per hour respectively, so together they lay $\frac{h}{9}+\frac{h}{10}-10$ per hour together. Since they finish the chimney in $5$ hours, $h=5\left( \frac{h}{9}+\frac{h}{10}-10 \right)$. Thus, $h=900 $. $\fbox{900}$.

Answer: 900