2008 AMC 10B Problem 18

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

Let

n

be the number of bricks; their solo rates are

\tfrac{n}{9}

and

\tfrac{n}{10}

Together they lay

\tfrac{n}{9}+\tfrac{n}{10}-10

bricks per hour for

5

hours to total

n

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.

Problem 18 in other years