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

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Joined: 03 Jan 2006
Posts: 28
A does half as much work as B in three-fourth of the time. If together  [#permalink]

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05 Feb 2007, 10:27
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Difficulty:

35% (medium)

Question Stats:

73% (02:08) correct 27% (03:49) wrong based on 11 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. 10 days
B. 15 days
C. 20 days
D. 30 days
E. 45 days
VP
Joined: 09 Jan 2007
Posts: 1043
Location: New York, NY
Schools: Chicago Booth Class of 2010
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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05 Feb 2007, 11:15
1
sravan_m444 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?

1/A+1/B=1/18
With some algebra= A+B=A*B/18

B does the Work (W) for a time T while
A does W/2 in 3/4T, for the whole Time (T) A would make 2W/3
So A equals 2B/3

2B/3 + B = 2B/3 * B /18

B=45
A=30
Manager
Joined: 10 Dec 2005
Posts: 110
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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05 Feb 2007, 14:27
Let's say B takes Xdays to finish 1 job, then
A will take 3/4(X) days to finish 0.5 job.

Now we know that

18(1/X + 0.5/0.75X) = 1

1/X + 50/75X = 1/18

1/X (1 + 10/15) = 1/18

X = 30
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Joined: 12 Feb 2006
Posts: 114
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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05 Feb 2007, 20:38
I wouldn't mind a little help with this because I got stuck and I am TERRIBLE at word translations.

For me, I did R x 3/4 = 1/2 x 1
Factor it to R = 2/3 or A's rate is 2/3 B

Now I'm confused how to set up the rest.

Amorpheus or Kwam,

Can you walk me through why you set it up like you did?

Thanks,
Manager
Joined: 10 Dec 2005
Posts: 110
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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06 Feb 2007, 04:21
bz9 wrote:
I wouldn't mind a little help with this because I got stuck and I am TERRIBLE at word translations.

For me, I did R x 3/4 = 1/2 x 1
Factor it to R = 2/3 or A's rate is 2/3 B

Now I'm confused how to set up the rest.

Amorpheus or Kwam,

Can you walk me through why you set it up like you did?

Thanks,

You did find the rate relation correction... Now in the question it is given that if both A and B were to work together the job will be done 18 days meaning,

Rate of A + Rate of B = 1/18 job/day

2/3 B + B = 1/18 job/day (this I got from the equation that you found out marked in RED above)

5/3 B = 1/18 job/day

B = 1/30 job/day

This mean it will take B 30 days to finish the job.

Let me know if you still have any questions.
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"Live as if you were to die tomorrow. Learn as if you were to live forever." - Mahatma Gandhi

Manager
Status: Post MBA, working in the area of Development Finance
Joined: 09 Oct 2006
Posts: 158
Location: Africa
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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06 Feb 2007, 09:15
kwam wrote:
sravan_m444 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?

1/A+1/B=1/18
With some algebra= A+B=A*B/18

B does the Work (W) for a time T while
A does W/2 in 3/4T, for the whole Time (T) A would make 2W/3
So A equals 2B/3

2B/3 + B = 2B/3 * B /18

B=45
A=30

As per the question, shouldn't A be taking more time than being taken by B?
Manager
Joined: 10 Dec 2005
Posts: 110
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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06 Feb 2007, 09:29
Artemov wrote:
kwam wrote:
sravan_m444 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?

1/A+1/B=1/18
With some algebra= A+B=A*B/18

B does the Work (W) for a time T while
A does W/2 in 3/4T, for the whole Time (T) A would make 2W/3
So A equals 2B/3

2B/3 + B = 2B/3 * B /18

B=45
A=30

As per the question, shouldn't A be taking more time than being taken by B?

The thing in red is wrong...
If A is the rate at which A is working and B is the rate at which B is working then...

A + B = 1/18 job/day

Now plug the values you found...
2B/3 + B = 1/18 job/day
5B/3 = 1/18 job/day

and hence B = 30 and A = 45
_________________

"Live as if you were to die tomorrow. Learn as if you were to live forever." - Mahatma Gandhi

VP
Joined: 09 Jan 2007
Posts: 1043
Location: New York, NY
Schools: Chicago Booth Class of 2010
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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08 Feb 2007, 02:18
1
amorpheus wrote:
Artemov wrote:
kwam wrote:
sravan_m444 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?

1/A+1/B=1/18
With some algebra= A+B=A*B/18

B does the Work (W) for a time T while
A does W/2 in 3/4T, for the whole Time (T) A would make 2W/3
So A equals 2B/3

2B/3 + B = 2B/3 * B /18

B=45
A=30

As per the question, shouldn't A be taking more time than being taken by B?

The thing in red is wrong...
If A is the rate at which A is working and B is the rate at which B is working then...

A + B = 1/18 job/day

Now plug the values you found...
2B/3 + B = 1/18 job/day
5B/3 = 1/18 job/day

and hence B = 30 and A = 45

Ops guys, you're right, and probably we would find both answers there, so I would have missed some points

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Posts: 8759
Re: A does half as much work as B in three-fourth of the time. If together  [#permalink]

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24 Oct 2018, 22:13
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Re: A does half as much work as B in three-fourth of the time. If together &nbs [#permalink] 24 Oct 2018, 22:13
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