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Jessica and Darren are painting a fence. Working alone at his constant

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Jessica and Darren are painting a fence. Working alone at his constant  [#permalink]

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New post 24 Sep 2018, 22:04
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Question Stats:

89% (01:33) correct 11% (02:18) wrong based on 34 sessions

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Jessica and Darren are painting a fence. Working alone at his constant, independent rate for one hour, Darren paints 1/6 of the fence before Jessica joins him and paints at her own constant rate until the fence is done. If Jessica and Darren paint together for 2 hours before the job is complete, how many hours would it have taken Jessica to paint the fence alone?


A. 4 hours

B. 14/3 hours

C. 5 hours

D. 16/3 hours

E. 6 hours

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Re: Jessica and Darren are painting a fence. Working alone at his constant  [#permalink]

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New post 24 Sep 2018, 22:36
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Bunuel wrote:
Jessica and Darren are painting a fence. Working alone at his constant, independent rate for one hour, Darren paints 1/6 of the fence before Jessica joins him and paints at her own constant rate until the fence is done. If Jessica and Darren paint together for 2 hours before the job is complete, how many hours would it have taken Jessica to paint the fence alone?


A. 4 hours

B. 14/3 hours

C. 5 hours

D. 16/3 hours

E. 6 hours


Darren paints 1/6 in 1 hours which is his rate

Jessica and darren paint for 2 more hours to finish (1-1/6) = 5/6 work

But Darren's 2 hours contribution in 5/6 work = 2/6 = 1/3
i.e. Jessica's contribution = (5/6)-(1/3) = 3/6 = 1/2

i.e. Jessica paint's 1/2 wall in 2 hours

i.e. She will paint entire wall in 4 hours

Answer: Option A
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Re: Jessica and Darren are painting a fence. Working alone at his constant  [#permalink]

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New post 24 Sep 2018, 22:48
2
Bunuel wrote:
Jessica and Darren are painting a fence. Working alone at his constant, independent rate for one hour, Darren paints 1/6 of the fence before Jessica joins him and paints at her own constant rate until the fence is done. If Jessica and Darren paint together for 2 hours before the job is complete, how many hours would it have taken Jessica to paint the fence alone?


A. 4 hours

B. 14/3 hours

C. 5 hours

D. 16/3 hours

E. 6 hours


Darren paints 1/6th of the wall in 1 hr so he will paint 2/6th of the wall in the next 2 hrs.
Total he does 1/6 + 2/6 = 3/6 = 1/2 of the work.

So Jessica does the other 1/2 work for which she takes 2 hrs.
For 1 complete work done independently, Jessica will take 4 hrs.

Answer (A)
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Re: Jessica and Darren are painting a fence. Working alone at his constant  [#permalink]

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New post 24 Sep 2018, 23:09
Ans: 4 hours

Solution:
In one hr. Darren do 1/6 part
__________ together do 5/12 part
so jesica do 1/4 part in one hr.
Therefore total work will be done by jesica in 4 hours

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Re: Jessica and Darren are painting a fence. Working alone at his constant  [#permalink]

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New post 24 Sep 2018, 23:09
Solution :-

#Shortcut


Let the work be 60 units

Darren's work rate : 10 units per hour
Jessica's work rate : x units per hour

Given :-


Amount of work left for both of them to complete as a team : 60 -(10)(1)=50 units

after working for 2 hours together work gets done .

2(10+x)=50
x=15 units per hour

Time taken by Jessica : 60/15= 4 Hours


Answer : A
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Re: Jessica and Darren are painting a fence. Working alone at his constant  [#permalink]

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New post 25 Sep 2018, 04:37
1
work done- 1/6
remaining- 5/6

they both work for 2 hours together so-

2(1/6+1/x)=5/6
Solving for x, you get x=4

(1/6 & 1/x= work done by Darren and Jessica in 1 hour)
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Re: Jessica and Darren are painting a fence. Working alone at his constant &nbs [#permalink] 25 Sep 2018, 04:37
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