AMC 10 Step by Step
Log inSign up
Printable

2008 AMC 10B Problem 18

Problem onlyBack to the problem
2008 AMC 10B Problem 18AMC 10 Step by Step
Name:                             Date: September 13, 2026
Linear Equations & Word Problems · difficulty 3 of 5 · about 3 min · position P16-20

Bricklayer Brenda would take nine hours to build a chimney alone, and Bricklayer Brandon would take 1010 hours to build it alone. When they work together, they talk a lot, and their combined output decreases by 1010 bricks per hour. Working together, they build the chimney in 55 hours. How many bricks are in the chimney?

  1. A)

    500500

  2. B)

    900900

  3. C)

    950950

  4. D)

    10001000

  5. E)

    19001900

Answer

B

Key insight

In bricks per hour the rates are N/9 and N/10; together minus 10 they equal N/5, and 1/9 + 1/10 - 1/5 = 1/90 gives N = 900.

Solution

Let the chimney contain NN bricks. Brenda lays N9\tfrac{N}{9} bricks per hour and Brandon lays N10\tfrac{N}{10} bricks per hour. Together, after the 1010-brick-per-hour loss, their rate is N9+N10−10\tfrac{N}{9} + \tfrac{N}{10} - 10. Finishing in 55 hours means this rate equals N5\tfrac{N}{5}:
N9+N10−10=N5.\frac{N}{9} + \frac{N}{10} - 10 = \frac{N}{5}.
Multiply through by 9090:
10N+9N−900=18N⟹N=900.10N + 9N - 900 = 18N \quad\Longrightarrow\quad N = 900.
Check: 100+90−10=180100 + 90 - 10 = 180 bricks per hour, and 5⋅180=9005 \cdot 180 = 900.

The answer is (B) 900\boxed{\textbf{(B)}\ 900}.

Why this works

Work problems become linear equations once everything is expressed as a rate. Because the slowdown is stated in bricks per hour, the rates must be in bricks per hour too, which is why the unknown NN appears in the rates rather than in a "fraction of the job" setup. Match the units of the given perturbation and the equation writes itself.

Alternative approach

Test the choices: with N=900N = 900, Brenda's rate is 100100, Brandon's 9090, combined 190−10=180190 - 10 = 180, and 900/180=5900/180 = 5 hours. The other choices fail this check.

The trap

Subtracting 10 bricks from the whole job instead of from the hourly rate, or dropping the reduction and finding the rates do not add up.

Common mistakes

  • Subtracting 10 bricks from the whole job instead of from the hourly rate, or dropping the reduction and finding the rates do not add up.
  • Adding the 1010 instead of subtracting, which produces N=−900N = -900 and a sign confusion.

Techniques

Set up the equation/formula and compute; no special trick needed