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

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14 Jul 2007, 18:58

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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?

Re: A and B working together can finish a job in d days. If A [#permalink]

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15 Apr 2012, 18:29

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, 18:39, edited 1 time in total.

Re: A and B working together can finish a job in d days. If A [#permalink]

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15 Apr 2012, 18:36

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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?

Re: A and B working together can finish a job in d days. If A [#permalink]

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15 Apr 2012, 21:40

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

Please solve it with your intellectual prowess!

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)

simplification leads to

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 _________________

Regards, Harsha

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

Re: A and B working together can finish a job in d days. If A [#permalink]

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16 Apr 2012, 00:36

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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

Please solve it with your intellectual prowess!

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: \(\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}\).

Re: A and B working together can finish a job in d days. If A [#permalink]

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17 Jun 2014, 09:59

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]

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18 Aug 2015, 09:21

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]

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23 Dec 2015, 06:03

Bunuel wrote:

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

Please solve it with your intellectual prowess!

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: \(\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}\).

Answer: C.

Could you please show the expanded form as to how to solve for d please? Thank you.

Re: A and B working together can finish a job in d days. If A [#permalink]

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23 Dec 2015, 06:13

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Expert's post

saiesta wrote:

Bunuel wrote:

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

Please solve it with your intellectual prowess!

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: \(\frac{1}{15+5}+\frac{1}{15+45}=\frac{1}{20}+\frac{1}{60}=\frac{1}{15}\).

Answer: C.

Could you please show the expanded form as to how to solve for d please? Thank you.

1 thing I would mention here as Bunuel has mentioned as well, you need to be intelligent to pick your battles in GMAT. It is not about finding the correct answer but you also need to make sure that you do not spend more time than what you should be spending.

Putting in the values in the options after you get 1/(d+5) + 1/(d+45) = 1/d , is the fastest way to solve this equation.

But for the sake of your question, look below for the solution:

1/(d+5) + 1/(d+45) = 1/d ---> \(\frac{(2d+50)}{(d+5)(d+45)} = \frac{1}{d}\) ---> \(2d^2+50d=d^2+50d+225\) ---> \(d^2=225\) --->\(d = \pm 15\), you can not have d < 0 as the number of days can only be >0.

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