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# Bricklayer Brenda would take 9 hours to build a chimney alone, and bri

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Joined: 02 Sep 2009
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Bricklayer Brenda would take 9 hours to build a chimney alone, and bri  [#permalink]

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27 Mar 2019, 21:16
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Difficulty:

55% (hard)

Question Stats:

60% (02:57) correct 40% (03:14) wrong based on 20 sessions

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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

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Re: Bricklayer Brenda would take 9 hours to build a chimney alone, and bri  [#permalink]

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27 Mar 2019, 21:59
1
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 BBN

BB 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)
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Re: Bricklayer Brenda would take 9 hours to build a chimney alone, and bri  [#permalink]

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27 Mar 2019, 23:44
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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

Rate of work of Brenda = 1/9
Rate of work of Brandon = 1/10
Combined rate should be 1/9 + 1/10 = 19/90 but it is actually 1/5

Decrease in rate = 19/90 - 1/5 = 1/90th of the chimney per hour.

But we are given that the decrease in rate is actually 10 bricks per hour so 10 bricks = 1/90th of chimney
No of bricks in the chimney = 10*90 = 900 bricks

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Re: Bricklayer Brenda would take 9 hours to build a chimney alone, and bri  [#permalink]

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28 Mar 2019, 02:48
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

rate of Brenda = 1/9
and Brandon= 1/10
together = 1/9+1/10; 19/90
they can build together at 1/5 hrs ; 19/90-1/5 ; 1/90 so rate = 90 and time = 10 hrs
work done = 90*10 ; 900
IMO B
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Re: Bricklayer Brenda would take 9 hours to build a chimney alone, and bri   [#permalink] 28 Mar 2019, 02:48
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