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Three surgeons - Anna, Claire, and Diane - are asked to perform an eme
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14 Jul 2020, 03:59
14 Jul 2020, 03:59
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A
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E
Difficulty:
45%
(medium)
Question Stats:
76% (03:15) correct
24%
(03:48)
wrong
based on 100
sessions
Three surgeons - Anna, Claire, and Diane - are asked to perform an emergency appendectomy. Working alone, Anna could complete the operation in 8 hours. Claire could do the job in 10 hours, while it would take Diane 12 hours by herself. On this particular shift, all three of the surgeons worked together on the appendectomy for two hours. At that point, Diane left to answer a page and never returned. An hour later, Claire left to handle another emergency - she also never returned. How long (in minutes) did it take Anna to complete the appendectomy, after
Claire and Diane both left?
A. 56
B. 60
C. 66
D. 70
E. 76
Claire and Diane both left?
A. 56
B. 60
C. 66
D. 70
E. 76
Re: Three surgeons - Anna, Claire, and Diane - are asked to perform an eme
[#permalink]
14 Jul 2020, 06:04
14 Jul 2020, 06:04
1
Kudos
If one of the experts can please confirm my logic please 
R --> Rate
A,B,D --> Anna, Claire, Diane respectively
R(A) = 1/8 ; R(B) = 1/10 ; R(D) = 1/12
Combined rate is the sum of all their rates = (15+12+10)/120 = 37/120 --> When all 3 are working
Combined rate is the sum of all their rates = (15+12)/120 = 27/120 --> When only Claire and Anna are working
37/120 * 2 + 27/120 * 1 = 101/120 of the work is completed by the time Anna is left alone
So she has to complete 19/120 of the operation with her rate of 1/8. (19/120) *(8/1) = 19/15 of an hour to complete. (19/15)* 60(minutes in an hour) = 76
IMO E
Does any of the experts know of a faster way than this multiplying and looking for LCMs?
R --> Rate
A,B,D --> Anna, Claire, Diane respectively
R(A) = 1/8 ; R(B) = 1/10 ; R(D) = 1/12
Combined rate is the sum of all their rates = (15+12+10)/120 = 37/120 --> When all 3 are working
Combined rate is the sum of all their rates = (15+12)/120 = 27/120 --> When only Claire and Anna are working
37/120 * 2 + 27/120 * 1 = 101/120 of the work is completed by the time Anna is left alone
So she has to complete 19/120 of the operation with her rate of 1/8. (19/120) *(8/1) = 19/15 of an hour to complete. (19/15)* 60(minutes in an hour) = 76
IMO E
Does any of the experts know of a faster way than this multiplying and looking for LCMs?
Re: Three surgeons - Anna, Claire, and Diane - are asked to perform an eme
[#permalink]
14 Jul 2020, 18:41
14 Jul 2020, 18:41
1
Kudos
Bunuel wrote:
Three surgeons - Anna, Claire, and Diane - are asked to perform an emergency appendectomy. Working alone, Anna could complete the operation in 8 hours. Claire could do the job in 10 hours, while it would take Diane 12 hours by herself. On this particular shift, all three of the surgeons worked together on the appendectomy for two hours. At that point, Diane left to answer a page and never returned. An hour later, Claire left to handle another emergency - she also never returned. How long (in minutes) did it take Anna to complete the appendectomy, after
Claire and Diane both left?
A. 56
B. 60
C. 66
D. 70
E. 76
Claire and Diane both left?
A. 56
B. 60
C. 66
D. 70
E. 76
Given:
1. Three surgeons - Anna, Claire, and Diane - are asked to perform an emergency appendectomy.
2, Working alone, Anna could complete the operation in 8 hours. Claire could do the job in 10 hours, while it would take Diane 12 hours by herself.
3. On this particular shift, all three of the surgeons worked together on the appendectomy for two hours. At that point, Diane left to answer a page and never returned. An hour later, Claire left to handle another emergency - she also never returned.
Asked: How long (in minutes) did it take Anna to complete the appendectomy, after Claire and Diane both left?
Operation done in first 2 hours = 2/8 + 2/10 + 2/12 = (30+24+20)/120 = 74/120
Operation done in next 1 hour = 1/8 + 1/10 = 9/40 = 27/120
Operation left to be done by Anna = 1 - 74/120 - 27/120 = (120-74-27)/120 = 19/120
Time taken by Anna to complete the Operation = 19*8*60/120 minutes = 19*4 = 76 minutes
IMO E
