Bunuel wrote:
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?
(A) 500
(B) 900
(C) 950
(D) 1000
(E) 1900
Let's call
Bricklayer Brenda as BB and
bricklayer Brandon as BBNBB completes the work in 9 hours
BBN completes the work in 10 hours
Let us assume the total work to be done as 900W( lcm of9,10)*10 ( Multiplied by 10 as there were other complications involved, so maybe a larger number will simplify calculation
Work per hour done by BB = 900W/9 = 100 W/h
Work per hour done by BBN = 900W/10= 90 W/h
Combined work if both did not waste time and work efficiently= 190 W/h
But we know that total work was completed in 5 hours, Hence, the actual work done per hour by BB+ BBN= 900W/5 = 180 W
The difference between actual work and work expected from BB=BBN = 190W - 180W = 10W
We know their
combined output give 10 bricks less per hour. This means 10W= 10 bricks
W= 1 brick ....(1)
Total work for chimney construction = 900W =
900 bricks (Subtituting from (1) above)
Correct Answer (B)