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# A and B working together can finish a job in d days. If A

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A and B working together can finish a job in d days. If A [#permalink]  14 Jul 2007, 17:58
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A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

A. 25
B. 60
C. 15
D. 14
E. 13

[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Apr 2012, 23:35, edited 2 times in total.
Edited the question and added the OA
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Re: A and B working together can finish a job in d days. If A [#permalink]  15 Apr 2012, 17:29
Sorry to revisit an old post but this was a toughy! Its not a necessary condition that d be an integer.

So working together they can do the job is d days.
Let $$r_1$$ be the rate of A
Let $$r_2$$ be the rate of B

Working together their rates to do the job is
Equation1:
$$(r_1+r_2)d=1 (job)$$

A working alone can do the job by
Equation2:
$$(r_1)(d+5)=1 (job)$$

B working alone can do the job by
Equation3:
$$(r_2)(d+45)=1 (job)$$

Now set the first equation to the second equation

$$(r_1+r_2)d=1 = (r_1)(d+5)$$ solve for d to get $$d=5(r_1/r_2)$$

Now set equation1 to equation2

$$(r_1)(d+5)=1 =(r_2)(d+45)$$ solve to get $$r_1/r_2=(d+45)/(d+5)$$

Now substitute $$d=5(r_1/r_2)=5((d+45)/(d+5))$$

to get $$d(d+5)=5(d+45)$$

which leads you to $$d^2=5*45$$. Which is equal to $$d=15$$ when you square root both sides (of couse d must be positive, were talking about days here!).

Again, tough problem. If anyone has an easier method let us know.

Last edited by alphabeta1234 on 15 Apr 2012, 17:39, edited 1 time in total.
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Re: A and B working together can finish a job in d days. If A [#permalink]  15 Apr 2012, 17:36
3
KUDOS
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25
(2) 60
(3) 15
(4) 14
(5) 13

1/(d+5) +1/(d+45)= 1/d
=> (2d+50)d = (d+5)*(d+45)
=> d^2 = 9*5*5
=> d= 15

hence option C.
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Re: A and B working together can finish a job in d days. If A [#permalink]  15 Apr 2012, 20:40
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25
(2) 60
(3) 15
(4) 14
(5) 13

take the total work as X

so both A & B can do it in d days, A alone in d+5 and B alone in d+45

rate calculation is total rate = sum of individual rates

X/d = X/(d+5) + X/(d+45)

we can remove X, then the equation becomes as below

1/d = 1/(d+5) + 1/(d+45)

d^2 = 225

d= + or - 15

u cannot have days in negative right as it should take some time to do a task...hence 15 is the answer...

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat
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Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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Re: A and B working together can finish a job in d days. If A [#permalink]  15 Apr 2012, 23:36
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Expert's post
Himalayan wrote:
A and B working together can finish a job in d days. If A works alone and completes the job, he will take d + 5 days. If B works alone and completes the same job, he will take d + 45 days. What is d?

(1) 25
(2) 60
(3) 15
(4) 14
(5) 13

If A works alone and completes the job, he will take d + 5 days --> the rate of A is $$\frac{1}{d+5}$$ job/day;
If B works alone and completes the job, he will take d + 45 days --> the rate of B is $$\frac{1}{d+45}$$ job/day;

Since A and B working together can finish a job in d days, then their combined rate is $$\frac{1}{d}$$ job/day;

So, $$\frac{1}{d+5}+\frac{1}{d+45}=\frac{1}{d}$$. At this point it's MUCH better to substitute the values from the answer choices rather than to solve for $$d$$.

Answer choice C fits: $$\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$$.

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Re: A and B working together can finish a job in d days. If A [#permalink]  25 Dec 2012, 20:21
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There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something .
To find X , use the formula X=$$\sqrt{ab}$$

X=$$\sqrt{5*45}$$
X= 15 days

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Re: A and B working together can finish a job in d days. If A [#permalink]  23 Jan 2013, 22:56
thinktank wrote:
There is always a trick to such Qs when your given A+B= x days , A= x+ something , B=x+ something .
To find X , use the formula X=$$\sqrt{ab}$$

X=$$\sqrt{5*45}$$
X= 15 days

What is the source of this trick? good one though.it can reduce the time to ans tremendously
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Re: A and B working together can finish a job in d days. If A [#permalink]  24 Jan 2013, 00:47
I was going through this 9th grade math text book to pick up on my basics, found a number of shortcuts there
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Re: A and B working together can finish a job in d days. If A [#permalink]  24 Jan 2013, 11:16
1/A = 1/(d+5)
1/B = 1/(d+45)

therefore... 1/(d+5) + 1/(d+45) = 1/d

When you do the math you end up with d^2 = 225. Therefore, d=15
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Re: A and B working together can finish a job in d days. If A [#permalink]  24 Jan 2013, 12:09
at bunuel..but solving for d is mathematically correct..then why is it that our answer is C
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Re: A and B working together can finish a job in d days. If A [#permalink]  25 Jan 2013, 04:40
Expert's post
chiccufrazer1 wrote:
:shock: at bunuel..but solving for d is mathematically correct..then why is it that our answer is C

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Re: A and B working together can finish a job in d days. If A [#permalink]  25 Jan 2013, 13:41
Ow!wow i now get you..it is still the same whether we solve for d or we plugin the answer choices..the only difference is that plugin method is saving us time:-)
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Re: A and B working together can finish a job in d days. If A [#permalink]  17 Jun 2014, 08:59
Hello from the GMAT Club BumpBot!

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Re: A and B working together can finish a job in d days. If A [#permalink]  18 Aug 2015, 08:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A and B working together can finish a job in d days. If A   [#permalink] 18 Aug 2015, 08:21
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# A and B working together can finish a job in d days. If A

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