Question

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?

$500$

$900$

$950$

$1000$

$1900$

Solution:

Let $n$ be the number of bricks. Brenda lays $\tfrac{n}{9}$ per hour and Brandon $\tfrac{n}{10},$ so together they lay $\tfrac{n}{9}+\tfrac{n}{10}-10$ per hour.

Over $5$ hours this equals $n:$ $5\left(\tfrac{n}{9}+\tfrac{n}{10}-10\right)=n.$ Solving, $\tfrac{5n}{9}+\tfrac{n}{2}-50=n,$ which gives $n=900.$

Thus, the correct answer is B.

2008 AMC 10B Problem 18

Solution:

Problem 18 in Other Years