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# Working alone at their respective constant rates, A can complete a tas

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Intern
Joined: 19 Dec 2014
Posts: 35
Working alone at their respective constant rates, A can complete a tas [#permalink]

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08 Sep 2015, 12:20
8
11
00:00

Difficulty:

95% (hard)

Question Stats:

56% (02:55) correct 44% (05:05) wrong based on 108 sessions

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Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?

A. 46/9
B. 50/9
C. 50/11
D. 36/7
E. 210/41
Manager
Joined: 10 Aug 2015
Posts: 103
Re: Working alone at their respective constant rates, A can complete a tas [#permalink]

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08 Sep 2015, 13:21
3
Solution : Let work done by A and B in one day is p and q respectively.
Then, work done by A and B together is p+q.
So, no. of days they have work for completion,n = 1/(p+q)

In first case, A worked for 6 days and B for 4 days ==> 6p + 4q = 1 -->(1)
In second case, A worked for 4.5 days and B for 6 days ==> 4.5p + 6q = 1 -->(2)
Solving (1)and(2) ==> p=1/9 and q=1/12. ==> p+q = 7/36
n = 1/(7/36) = 36/7

Option,D
Intern
Joined: 03 Feb 2014
Posts: 38
Location: United States
Concentration: Entrepreneurship, General Management
WE: General Management (Other)
Re: Working alone at their respective constant rates, A can complete a tas [#permalink]

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08 Sep 2015, 14:02
1
Work done by A & B in a day = x & y respectively.
When A starts:
No. of days when A works = 6 & No. of days when A works = 4 → 6x + 4y = 1
When B starts:
No. of days when A works = 4.5 & No. of days when A works = 6 → 4.5x + 6y = 1
Solving the above two equations for x & y
x = 1/9 & y = 1/12
→ Total work done by A & B in a day = 1/9 + 1/12 = 7/36
→ No. of days to complete the work when both work together = 36/7;
_________________

--Shailendra

VP
Joined: 07 Dec 2014
Posts: 1018
Working alone at their respective constant rates, A can complete a tas [#permalink]

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25 Dec 2016, 15:46
Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?

A. 46/9
B. 50/9
C. 50/11
D. 36/7
E. 210/41

6/a+4/b=4.5/a+6/b
a/b=3/4
inversely, rate of A/B=4/3
combined rate of A+B=4/x+3/x=7/x
inverting back to time, only answer choice with 7 in denominator is 36/7
D
Intern
Joined: 17 Apr 2016
Posts: 4
Re: Working alone at their respective constant rates, A can complete a tas [#permalink]

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15 Sep 2017, 06:01
d)
A work- a
B work- b
Accrdng to the eq
6b+4a=4.5b+6a
1.5b=2a
a/b=3/4
This means a do 3 units of work and b do 4 units of work.
Put in eq 6b+4a=36
combined work -7
Ans 36/7
Re: Working alone at their respective constant rates, A can complete a tas   [#permalink] 15 Sep 2017, 06:01
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