2008 AMC 10B Problem 18

Bricklayer Brenda would take nine 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 decreases by 10 bricks per hour. Working together, they build the chimney in 5 hours. How many bricks are in the chimney?

\mathrm{(A)}\ 500\qquad\mathrm{(B)}\ 900\qquad\mathrm{(C)}\ 950\qquad\mathrm{(D)}\ 1000\qquad\mathrm{(E)}\ 1900

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.