If 3 people work together, how long will the job take?

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AndreaV424: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Fri Jul 10, 2009 4:38 pm; Location: Phoenix; Thanked: 2 times

by AndreaV424 » Thu Jul 16, 2009 6:23 pm

9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

A. 2 minutes and 44 seconds
B. 2 minutes and 58 seconds
C. 3 minutes and 10 seconds
D. 3 minutes and 26 seconds
E. 4 minutes and 15 seconds

---------------------------------
I calculated that the following

Steven can mix 4 drinks per min
Sue can mix 2 drinks per min
Jack can mix 4/3 drinks per min

Together they make 22/3 or 7 1/3 drinks per minute

I am stuck between answer A and B. How can I calculate the correct second? Should I convert into seconds (see how many second 1 drink takes to make)?

The correct answer is A. I appreciate any help and clarification. Thank you!

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Source: Beat The GMAT — Problem Solving | Thu Jul 16, 2009 6:23 pm

tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Thu Jul 16, 2009 6:30 pm

this is how I solved
first thing I noticed is is time for everyone. So i took the LCM and many drinks each of them can make in that time
LCM is 30 minutes
Steve makes 120 drinks in 30 min
Sue makes 60 drinks in 30 mins
Jack makes 40 drinks in 30 mins

so total 220 drinks in 30 mins
20 drinks in 30/11 min i.e A

The powers of two are bloody impolite!!

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truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Thu Jul 16, 2009 6:44 pm

S= The time it takes Steve to mix 20 drinks.

U= The time it takes Sue to mix 20 drinks.

J= The time it takes Jack to mix 20 drinks.

X= The time it takes Steven, Sue, and Jack, working together to mix 20 drinks.

1/S+1/U+1/J=1/X

1/5+1/10+1/15=1/X

6/30+3/30+2/30=1/X

11/30=1/X

30/11=X

30/11 minutes= 2 minutes and 44 secs.

A

Last edited by truplayer256 on Thu Jul 16, 2009 6:44 pm, edited 1 time in total.

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gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pmFollowed by: 17 members; Location: Paris, France; Thanked: 71 times; GMAT Score:710

by gmat740 » Thu Jul 16, 2009 6:44 pm

Here is a very quick way of solving this one.
Look at the question

9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

all are do the same amount of work but take different amount of time

so,use the theory of work-time:

1/5 + 1/10 +1/15 = 1/T

where T= time taken, when all work together

T= 30/11

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: If 3 people work together, how long will the job take?

by Ian Stewart » Thu Jul 16, 2009 7:25 pm

AndreaV424 wrote: A. 2 minutes and 44 seconds
B. 2 minutes and 58 seconds
C. 3 minutes and 10 seconds
D. 3 minutes and 26 seconds
E. 4 minutes and 15 seconds

---------------------------------
I calculated that the following

Steven can mix 4 drinks per min
Sue can mix 2 drinks per min
Jack can mix 4/3 drinks per min

Together they make 22/3 or 7 1/3 drinks per minute

I am stuck between answer A and B. How can I calculate the correct second? Should I convert into seconds (see how many second 1 drink takes to make)?

The correct answer is A. I appreciate any help and clarification. Thank you!

There are some good solutions above, so I'll just add a couple of comments:

-you correctly arrived at their rate per minute - they make 7 1/3 drinks each minute. If at this stage you were stuck, you could at least make an estimate:

* after 1 minute, they will have made 7 1/3 drinks
* after 2 minutes, they will have made 14 2/3 drinks
* after 3 minutes, they will have made 22 drinks

So it must take them less than 3 minutes to make 20 drinks, and it certainly doesn't take them 2m58 seconds to make exactly 20 drinks, because that would mean they make 2 drinks in the 2 seconds between 2m58s and 3m00s. There's no partial credit on the GMAT, but if you get partway through a problem, and you're confident your work is correct, you may be able to use that work to at least eliminate some wrong answers, or in this question, pick the correct answer.

That said, I don't care for the question. As a few people established above, the answer is 30/11 minutes. That isn't 2m44s; it's 2m43.6363... seconds. In any real GMAT question, if the answers are rounded off, or are approximations, the question will say as much. Where is the question from?

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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rangerguy2000: Senior | Next Rank: 100 Posts; Posts: 90; Joined: Thu Aug 07, 2008 4:46 pm; Location: Toronto, Canada; Thanked: 3 times; GMAT Score:620

how

by rangerguy2000 » Thu Jul 16, 2009 8:22 pm

Ok, i got upto 2 mins as the ans... but how do u calculate if it is 44 secs or 58 secs?

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truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Fri Jul 17, 2009 6:37 am

Ok, i got upto 2 mins as the ans... but how do u calculate if it is 44 secs or 58 secs?

30/11 is known as an improper fraction. Let's say that we have an improper fraction x/y and a mixed fraction z and n/y. In order to convert a mixed fraction into an improper fraction, we do (yz+n)/y. It's obvious in this case that yz+n=x.

Let's do the same thing for 30/11, but in this case, we have to do the reverse.

yz+n=30

z=2

y=11

30-22=n

8=n

So we know that 30/11 minutes is equivalent to 2 and 8/11 minutes.

1 minute equals 60 seconds, 8/11 of a minute equals 60*8/11 seconds or about 43.64 secs which is ~ 44 secs.

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AndreaV424: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Fri Jul 10, 2009 4:38 pm; Location: Phoenix; Thanked: 2 times

Thank you everyone!!

by AndreaV424 » Fri Jul 17, 2009 8:49 am

Thanks everyone for taking the time to response. Your input was very helpful!

I took another look at the problem. I was able to solve down to 30/11. From here I calculated that 30/11 = 2.73. Then I thought, what is 73/100 of 60 seconds?

73/100 * 60 = 219/5
219/5 = 44 seconds

----------------------
In case anyone is interested on how I got down to 30/11.
Together they make 22/3 drinks in 1 minutes. I set up cross-multiply equation.

22/3 drinks over 1 min = 20 drinks over "x"

= (22/3)x = 20
= x = 20 * (3/22) = 30/11

Happy Studying

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ghacker: Master | Next Rank: 500 Posts; Posts: 148; Joined: Wed Jun 03, 2009 8:04 pmFollowed by: 1 member; Thanked: 18 times

by ghacker » Fri Jul 17, 2009 9:57 am

If they work together they will take less time than the fastest person among the three ( unless they waste time chatting !!!!!!)

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

A. 2 minutes and 44 seconds
B. 2 minutes and 58 seconds
C. 3 minutes and 10 seconds
D. 3 minutes and 26 seconds
E. 4 minutes and 15 seconds

So we can clearly see that it must be less than 3 min hence B,C,D,E are out
We Two options left A and B

B is very close to 3 so it must be A

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