/A+1/B=5/6---(1)
1/A+1/C=2/3---(2)
1/B+1/C=1/2---(3)
(2)-(3)=1/A-1/B=1/6---(4)
(4)+(1)=2/A=1
A=2
Now substitute A into equations 1, 2, 3, or 4 to get B and C.
B=3
C=6
1/A+1/B+1/C=1/X
X= The number of hours it takes pumps A, B, and C, operating simultaneously to fill the tank
1/2+1/3+1/6=1/X
1=1/X
X=1 hour.
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water filling
Source: Beat The GMAT — Problem Solving |
Its a very simple question.
We have 3 equations from Work-time theory.
1/a + 1/b = 5/6
1/b + 1/c = 1/2
1/c +1/a = 2/3
add all the 3
2*(1/a + 1/b + 1/c) = 2
(1/a + 1/b + 1/c) = 1
so,answer 1 hr.
A point of advice, please revise some basic Quant concepts, so that you don't get caught up with these simple questions.
Hope this helps
We have 3 equations from Work-time theory.
1/a + 1/b = 5/6
1/b + 1/c = 1/2
1/c +1/a = 2/3
add all the 3
2*(1/a + 1/b + 1/c) = 2
(1/a + 1/b + 1/c) = 1
so,answer 1 hr.
A point of advice, please revise some basic Quant concepts, so that you don't get caught up with these simple questions.
Hope this helps
-
PussInBoots
- Master | Next Rank: 500 Posts
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When you add all the 3 three equations wriiten below:shibal wrote:gmat740, why do you multiply by 2 the addition?
LHS = (1/a +1/b) +( 1/b + 1/c) +(1/c +1/a )1/a + 1/b = 5/6
1/b + 1/c = 1/2
1/c +1/a = 2/3
We can see that we have 2(1/a) , 2(1/b) and 2(1/c)
thus it can be simplified as 2*(1/a +1/b +1/c)
Hope this Helps
shibal,
Think of the equations this way:
a + b = 5/6
a + c = 2/3
b + c = 1/2
where, a, b, and c represent the work rates of a, b, and c.
a + b + a + c + b + c = 5/6 + 2/3 + 1/2
2a + 2b + 2c = 5/6 + 4/6 + 3/6
2a + 2b + 2c = 12/6
2a + 2b + 2c = 2
This above equation tells us that it takes 2 of each of the workers 1/2 hour to complete the job. But, we only need one of each worker. Therefore factor the 2.
2(a + b + c) = 2
a + b + c = 1
Therefore, a, b, and c working together complete the job in 1 hour.
Think of the equations this way:
a + b = 5/6
a + c = 2/3
b + c = 1/2
where, a, b, and c represent the work rates of a, b, and c.
a + b + a + c + b + c = 5/6 + 2/3 + 1/2
2a + 2b + 2c = 5/6 + 4/6 + 3/6
2a + 2b + 2c = 12/6
2a + 2b + 2c = 2
This above equation tells us that it takes 2 of each of the workers 1/2 hour to complete the job. But, we only need one of each worker. Therefore factor the 2.
2(a + b + c) = 2
a + b + c = 1
Therefore, a, b, and c working together complete the job in 1 hour.
