Problem:
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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number of bricks in the chimney. Then the number of bricks per hour Brenda and Brandon can lay working alone is and , respectively. Working together they can lay bricks in an hour, or
bricks in 5 hours to complete the chimney. Thus
and the number of bricks in the chimney is .
OR
Suppose that Brenda can lay bricks in an hour and Brandon can lay bricks in an hour. Then the number of bricks in the chimney can be expressed as , , or . The equality of these expressions leads to the system of equations
It follows that , so the number of bricks in the chimney is .
The problems on this page are the property of the MAA's American Mathematics Competitions