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

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

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New post 05 Feb 2007, 10:27
2
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Difficulty:

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

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

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New post 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?
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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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New post 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
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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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New post 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 :oops:

Sorry about that.
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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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New post 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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