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A and B working together can finish a job in d days. If A [#permalink]
14 Jul 2007, 17:58

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

77% (03:21) correct
23% (02:28) wrong based on 278 sessions

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]
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.

Re: A and B working together can finish a job in d days. If A [#permalink]
15 Apr 2012, 17:36

3

This post received 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?

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

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]
15 Apr 2012, 23:36

4

This post received KUDOS

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]
17 Jun 2014, 08:59

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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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