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If Dave works alone he will take 20 more hours to complete a

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Director
Joined: 23 Jan 2013
Posts: 511
Schools: Cambridge'16
If Dave works alone he will take 20 more hours to complete a  [#permalink]

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02 Oct 2015, 23:50
Algebra:

1/(x+20) + 1/(x+5) = 1/x

x^2=100 => x=10, so 30/15=2/1

Guessing:

1) would narrow to B and E and because Dave works slower the David/Diana=2/1

2) need ratio x+20/x+5

go on picking number starting from 1 as x and compare with answer choices. So x=10 gives 30/15=2/1

B
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Joined: 27 Jun 2015
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Re: If Dave works alone he will take 20 more hours to complete a  [#permalink]

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23 Jul 2016, 01:54
shreyas wrote:
short cut for such problems:

time taken to complete the task working together = sqrt (20*5) = 10.
Dave takes 20 more hours = 10 + 20 = 30; Diane takes 5 more hours = 5 + 10 = 15.

Ratio = 30/15 = 2:1

Where does this equation come from? Can someone explain it in more detail please?
Thanks.
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Joined: 27 Jun 2015
Posts: 16
Re: If Dave works alone he will take 20 more hours to complete a  [#permalink]

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23 Jul 2016, 02:02
Got it... the formula comes from these equations.

ak1802 wrote:
For 1/(t+20)+1(t+5) = 1/t .... how does t = 10? I don't know how to calculate it.

Hey, I hope this helps:

[1/(t+5) ] + [1/(t+20)] = 1/t

(t+20+t+5) / [(t+5)*(t+20)] = 1/t

(t+5)*(t+20) = t(t+20) + t(t+5)

t^2 + 25t + 100 = t^2 + 20t + t^2 + 5t

100 = t^2

10 = t , plug 10 = t back into the original set-up.
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Re: If Dave works alone he will take 20 more hours to complete a  [#permalink]

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29 Aug 2016, 09:07
asimov wrote:
If Dave works alone he will take 20 more hours to complete a task than if he worked with Diana to complete the task. If Diana works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dave to complete the task? What is the ratio of the time taken by Dave to that taken by Diana if each of them worked alone to complete the task?

A. 4 : 1
B. 2 : 1
C. 10 : 1
D. 3 : 1
E. 1 : 2

Please find the solution as attached.
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Re: If Dave works alone he will take 20 more hours to complete a  [#permalink]

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14 Nov 2016, 02:36
mdfrahim wrote:
Lets say Dave takes 50 hrs.
then Dave + Diane takes 30 hrs.
Since Diane take 5 hrs less so she takes 25 hrs.

Ratio of Dave/Diane = 50/25 = 2/1.

Great, thank you! Very easy and straightforward.
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Re: If Dave works alone he will take 20 more hours to complete a  [#permalink]

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26 Dec 2016, 01:54
Let "x" be the rate of both Diana & Dave working together, then
1/(x+20) + 1/(x+5) = 1/x
Solving this equation gives us x equal to 10, thus x+20/x+5 = 2/1, Answer B.
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If Dave works alone he will take 20 more hours to complete a  [#permalink]

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06 Jun 2017, 17:34
asimov wrote:
If Dave works alone he will take 20 more hours to complete a task than if he worked with Diana to complete the task. If Diana works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dave to complete the task? What is the ratio of the time taken by Dave to that taken by Diana if each of them worked alone to complete the task?

A. 4 : 1
B. 2 : 1
C. 10 : 1
D. 3 : 1
E. 1 : 2

1. Let x be the time required when both work together
2. Dave's time is x+20 and Diana's time is x+5
3. 1/(x+20) + 1/(x+5) = 1/x
x=10. So the ratio is 30:15 or 2:1
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