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Working together, A and B can complete a work in 10 days, B and C can
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25 Apr 2023, 03:25
25 Apr 2023, 03:25
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82% (02:15) correct
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Working together, A and B can complete a work in 10 days, B and C can complete the same work in 12 days and A and C can complete that work in 15 days. If A, B and C are working together, how many days does it take to complete the work?
A. 5
B. 6
C. 7
D. 8
E. 9
A. 5
B. 6
C. 7
D. 8
E. 9
Re: Working together, A and B can complete a work in 10 days, B and C can
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04 May 2023, 09:49
04 May 2023, 09:49
1
A's rate = 1/a
B's rate = 1/b
C's rate = 1/c
1/a + 1/b = 1/10
1/b + 1/c = 1/12
1/a + 1/c = 1/15
Add the three equations:
2/a + 2/b + 2/c) = 15/60
2(1/a + 1/b + 1/c) = 1/4
Since we need A, B, and C to be working together, we need to divide both sides by 2:
(1/a + 1/b + 1/c) = 1/8
Their combined rate is 1/8, which means that together they will spend 8 hours working.
B's rate = 1/b
C's rate = 1/c
1/a + 1/b = 1/10
1/b + 1/c = 1/12
1/a + 1/c = 1/15
Add the three equations:
2/a + 2/b + 2/c) = 15/60
2(1/a + 1/b + 1/c) = 1/4
Since we need A, B, and C to be working together, we need to divide both sides by 2:
(1/a + 1/b + 1/c) = 1/8
Their combined rate is 1/8, which means that together they will spend 8 hours working.
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Working together, A and B can complete a work in 10 days, B and C can
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07 Sep 2024, 00:25
07 Sep 2024, 00:25
1
Let's assume following variables/values
Formula to be used Rate * Time = Work
A and B can complete a work in 10 days
=> Combined rate of A and B = A + B
=> Rate * Time = Work
=> (A + B) * 10 = 1
=> A + B = 1/10 ...(1)
B and C can complete the same work in 12 days
=> Combined rate of B and C = B + C
=> Rate * Time = Work
=> (B + C) * 12 = 1
=> B + C = 1/12 ...(2)
A and C can complete that work in 15 days
=> Combined rate of A and C = A + C
=> Rate * Time = Work
=> (A + C) * 15 = 1
=> A + C = 1/15 ...(3)
If A, B and C are working together, how many days does it take to complete the work?
=> Combined rate of A, B and C = A + B + C
=> Rate * Time = Work
=> (A + B + C) * Time = 1
=> Time = 1 / (A + B + C)
(1) + (2) + (3)
=> A + B + B + C + A + C = 1/10 + 1/12 + 1/15
=> 2 * (A + B + C) = 6/60 + 5/60 + 4/60 = 15/60 = 1/4
=> A + B + C = 1/(2*4) = 1/8
=> Time = 1/(A + B + C) = 1 / (1/8) = 8
So, Answer will be D
Hope it helps!
Watch following video to MASTER Work Rate Problems
- ◉ Rate of A = A
◉ Rate of B = B
◉ Rate of C = C
◉ Work Done = 1 (As Work done by everyone is same)
Formula to be used Rate * Time = Work
A and B can complete a work in 10 days
=> Combined rate of A and B = A + B
=> Rate * Time = Work
=> (A + B) * 10 = 1
=> A + B = 1/10 ...(1)
B and C can complete the same work in 12 days
=> Combined rate of B and C = B + C
=> Rate * Time = Work
=> (B + C) * 12 = 1
=> B + C = 1/12 ...(2)
A and C can complete that work in 15 days
=> Combined rate of A and C = A + C
=> Rate * Time = Work
=> (A + C) * 15 = 1
=> A + C = 1/15 ...(3)
If A, B and C are working together, how many days does it take to complete the work?
=> Combined rate of A, B and C = A + B + C
=> Rate * Time = Work
=> (A + B + C) * Time = 1
=> Time = 1 / (A + B + C)
(1) + (2) + (3)
=> A + B + B + C + A + C = 1/10 + 1/12 + 1/15
=> 2 * (A + B + C) = 6/60 + 5/60 + 4/60 = 15/60 = 1/4
=> A + B + C = 1/(2*4) = 1/8
=> Time = 1/(A + B + C) = 1 / (1/8) = 8
So, Answer will be D
Hope it helps!
Watch following video to MASTER Work Rate Problems
