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# A does half as much work as B in three-fourth of the time. If together

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
A does half as much work as B in three-fourth of the time. If together  [#permalink]

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30 Jan 2019, 02:59
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Difficulty:

45% (medium)

Question Stats:

69% (02:41) correct 31% (02:58) wrong based on 108 sessions

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A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it

A. 40 days
B. 35 days
C. 30 days
D. 25 days
E. 20 days

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Posts: 5031
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Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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30 Jan 2019, 03:33
1
Bunuel wrote:
A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it

A. 40 days
B. 35 days
C. 30 days
D. 25 days
E. 20 days

for A given
work
x/2 = 3/4 * ra
ra = 2x/3
rb= x

given together a & b can do work in 18 days
or say
2x/3 + x= 1/18
5x=1/6
x= 1/30
days of b = 30 days
IMO C
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Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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01 Feb 2019, 19:12
Bunuel wrote:
A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it

A. 40 days
B. 35 days
C. 30 days
D. 25 days
E. 20 days

We can let n = the number of days it takes B to complete the work by himself. Thus, B’s rate = 1/n and A’s rate = (1/2)/(3n/4) = 4/(6n) = 2/(3n). The sum of their individual rates is 1/18, and we create the equation:

2/(3n) + 1/n = 1/18

Multiplying by 18n, we have:

12 + 18 = n

30 = n

So it takes B 30 days to complete the job by himself.

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# Scott Woodbury-Stewart

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VP
Joined: 07 Dec 2014
Posts: 1224
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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01 Feb 2019, 21:09
Bunuel wrote:
A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it

A. 40 days
B. 35 days
C. 30 days
D. 25 days
E. 20 days

B's time to complete work alone=t
A's rate=(1/2)/(3t/4)=2/3t
18(2/3t+1/t)=1
t=30 days
C
Intern
Joined: 19 May 2019
Posts: 3
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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22 May 2019, 15:39
How rate is calculated

Posted from my mobile device
Senior Manager
Joined: 03 Mar 2017
Posts: 366
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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27 May 2019, 19:34
1
Abedyeasin111 wrote:
How rate is calculated

Posted from my mobile device

The work done by A is 1/2 of B. Apply formula W=R*T. Therefore R=W/T.

W=1/2 Work(B) and T=3/4 of Time(B)

R(A)=(1/2(WB))/(3/4)(TB)

R(A)=2/3(RB) because WB/TB= RB by same W=R*T formula.

2/3B+1/B=1/18-----Final equation

Solve and you will get B=30

Hope this helps.
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VP
Joined: 07 Dec 2014
Posts: 1224
A does half as much work as B in three-fourth of the time. If together  [#permalink]

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28 May 2019, 19:48
Bunuel wrote:
A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it

A. 40 days
B. 35 days
C. 30 days
D. 25 days
E. 20 days

let B do 12 units of work per hour
and A do 12/2+6/3=8 units per hour
so B/A rate ratio=12/8=3/2
hence, B completes 3/5 of the house alone in the 18 hours working with A
and completes the remaining 2/5 in 12 hours working alone
18+12=30
C
Intern
Joined: 14 May 2019
Posts: 5
A does half as much work as B in three-fourth of the time. If together  [#permalink]

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29 May 2019, 13:55
Given:
A + B = 1/18

Also Given:
A => B/2 * 3/4T
B => B * T

We want to get A in terms of T. Multiply (B/2)*(4/3) and (3/4T)*(4/3)

Now:
A => B(2/3) * T
B => B * T

Plug this into our first equation:
B + B(2/3) = 1/18
B = 1/30
B = 30 Days
Target Test Prep Representative
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Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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01 Jun 2019, 06:35
Bunuel wrote:
A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it

A. 40 days
B. 35 days
C. 30 days
D. 25 days
E. 20 days

If we let n = the total number of days for B to complete the work, the rate of B is 1/n.

The rate of A is (1/2)/(3n/4) = 4/(6n) = 2/(3n)

Since they take 18 days to complete the job:

18/n + (18)[2/(3n)] = 1

18/n + 12/n = 1

18 + 12 = n

30 = n

So it takes B 30 days to complete the job.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Joined: 23 Apr 2018
Posts: 139
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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01 Jun 2019, 07:58
1
warrior1991 wrote:
Abedyeasin111 wrote:
How rate is calculated

Posted from my mobile device

The work done by A is 1/2 of B. Apply formula W=R*T. Therefore R=W/T.

W=1/2 Work(B) and T=3/4 of Time(B)

R(A)=(1/2(WB))/(3/4)(TB)

R(A)=2/3(RB) because WB/TB= RB by same W=R*T formula.

2/3B+1/B=1/18-----Final equation

Solve and you will get B=30

Hope this helps.

Can you show how to solve this ? I am somehow unable to solve.

2/3B + 1/B = 18
I am taking
3B as their LCM

2+3/3B = 18

5/3B = 18
which is giving me 5 = 54B, and that's weird..please tell me, what's my mistake ?
Intern
Joined: 01 Jun 2019
Posts: 1
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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01 Jun 2019, 10:51
Shrey9 wrote:
warrior1991 wrote:
Abedyeasin111 wrote:
How rate is calculated

Posted from my mobile device

The work done by A is 1/2 of B. Apply formula W=R*T. Therefore R=W/T.

W=1/2 Work(B) and T=3/4 of Time(B)

R(A)=(1/2(WB))/(3/4)(TB)

R(A)=2/3(RB) because WB/TB= RB by same W=R*T formula.

2/3B+1/B=1/18-----Final equation

Solve and you will get B=30

Hope this helps.

Can you show how to solve this ? I am somehow unable to solve.

2/3B + 1/B = 18
I am taking
3B as their LCM

2+3/3B = 18

5/3B = 18
which is giving me 5 = 54B, and that's weird..please tell me, what's my mistake ?

You have to do the equation in terms of rate, so you set the equation to 1/18 (i.e. the rate), not 18 (the days).
Re: A does half as much work as B in three-fourth of the time. If together   [#permalink] 01 Jun 2019, 10:51
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