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Help with figuring out a math formula.

Old 03-11-08, 09:55 PM
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Help with figuring out a math formula.

Hi I haven't posted here in a long time. But have been lurking. I came across a few of these problems, all similar in style. here is an example of one:

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?

2 minutes and 44 seconds

2 minutes and 58 seconds

3 minutes and 10 seconds

3 minutes and 26 seconds

4 minutes and 15 seconds

No I was wondering if there is a formula for these types of problems or basically an example of how you solved this. I have been out of school now for over 5 years I used to never have a problem in math, guess. Thank you in advance
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Old 03-11-08, 09:57 PM
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Figure out how many drinks per minute each of them can do.

Then figure out how many drinks per minute all three of them together will do.

Then figure out how many minutes it will take to mix 20 drinks at that rate.
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Old 03-11-08, 10:06 PM
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Then figure out that none of those answers is correct.

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Old 03-11-08, 10:17 PM
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average, sum, average

Ŕ votre santé.
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Old 03-11-08, 10:22 PM
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The first answer is correct according to them.
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Old 03-11-08, 10:25 PM
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4x + 2x + (4/3)x = 20

Roughly 2 minutes and 44 seconds
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Old 03-11-08, 10:28 PM
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Thank You!
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Old 03-11-08, 10:32 PM
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Originally Posted by M2theAX
The first answer is correct according to them.
Not in my bar!

They're assuming drinks are mixed in such a uniform fashion that a partially mixed drink from one person can be combined with a partially mixed drink from another person to create a complete mixed drink. In reality, we know that's not true. Who puts the umbrella in?

The more "correct" answer is 3 minutes. Instead of figuring out how many drinks someone can mix in a unit of time, you should figure out how much time it takes to mix a single drink. Steven takes 15 seconds, Sue takes 30, and Jack takes 45. At 2:44, you only have 10 drinks from Steven, 5 from Sue, and 3 from Jack for a total of 18. Steven has 14/15 of a drink finished, Sue has 14/30, and Jack has 29/45, which is enough to combine for 2 more drinks, but that's real world dumb. In reality, Steven will finish the 19th drink at 2:45, and all 3 of them will finish a drink at 3:00 for a total of 22.

I'm just sayin' ...

das
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Old 03-11-08, 10:35 PM
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Point taken Das,

Now heres a curveball for you: Can the same logic be applied to following problem:

Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ˝ hours. How quickly can all three fill the pool together?

12 minutes
15 minutes
21 minutes
23 minutes
28 minutes
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Old 03-11-08, 10:40 PM
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Originally Posted by M2theAX
Point taken Das,

Now heres a curveball for you: Can the same logic be applied to following problem:

Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ˝ hours. How quickly can all three fill the pool together?

12 minutes
15 minutes
21 minutes
23 minutes
28 minutes
15 minutes

Same principle.

x = time (the answer)

(1 pool / 30 min.)*x + (1 pool / 45 min.)*x + (1 pool / 90 min.)*x = 1 pool
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Old 03-11-08, 10:42 PM
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The same logic should be applied to that problem. How much water is in a bucket or how many buckets does it take to fill the pool? There's a time overhead for each bucket (carrying distance, pouring time, etc). Sadly, enough real world information isn't provided, so you're pretty much forced to go along with their concept. The idea is to find a least common denominator, which is 180. Jim can fill 1/30 (or 6/180) in one minute, Sue 1/45 (or 4/180) and Tony 1/90 (or 2/180). Therefore, every minute, they fill (6+4+2)/180. 180/12 = 15.

If the question were properly worded, they'd be filling the pool with evenly flowing water hoses. Since the question explicitly says they're carrying buck(et)s, it's a bad question.

das
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Old 03-11-08, 10:45 PM
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Originally Posted by JasonF
Figure out how many drinks per minute each of them can do.

Then figure out how many drinks per minute all three of them together will do.

Then figure out how many minutes it will take to mix 20 drinks at that rate.
JasonF is basically right. But this problem is even easier than that since we are talking about a common, single job - namely making 20 drinks. Think of making 20 drinks as "1 job."

Then the overall time needed when everyone works together is:

Total Time = 1/(1/T1 + 1/T2 + 1/T3), where T1, T2 and T3 are the times IN COMMON UNITS.

So Total time = 1 /(1/5 + 1/10 + 1/15) [in units of minutes]
= 1 / (6/30 + 3/30 + 2/30) = 1 / (11/30)
= 30/11 minutes = 2 8/11 minutes
= 2 minutes and 44 seconds
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Old 03-11-08, 10:47 PM
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Originally Posted by M2theAX
Point taken Das,

Now heres a curveball for you: Can the same logic be applied to following problem:

Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ˝ hours. How quickly can all three fill the pool together?

12 minutes
15 minutes
21 minutes
23 minutes
28 minutes
= 1 / (1/30 + 1/45 + 1/90) [SAME UNITS]
= 1 / (3/90 + 2/90 + 1/90)
= 1 / (6/90)
= 90/6
= 15 minutes
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Old 03-11-08, 11:53 PM
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Just in case here is another one:

x - .20X = 12590


solve for x

Very easy maybe its just late at night and I'm getting tired

Last edited by M2theAX; 03-11-08 at 11:57 PM.
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Old 03-12-08, 08:21 AM
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Originally Posted by das Monkey
Not in my bar!

They're assuming drinks are mixed in such a uniform fashion that a partially mixed drink from one person can be combined with a partially mixed drink from another person to create a complete mixed drink. In reality, we know that's not true. Who puts the umbrella in?

The more "correct" answer is 3 minutes. Instead of figuring out how many drinks someone can mix in a unit of time, you should figure out how much time it takes to mix a single drink. Steven takes 15 seconds, Sue takes 30, and Jack takes 45. At 2:44, you only have 10 drinks from Steven, 5 from Sue, and 3 from Jack for a total of 18. Steven has 14/15 of a drink finished, Sue has 14/30, and Jack has 29/45, which is enough to combine for 2 more drinks, but that's real world dumb. In reality, Steven will finish the 19th drink at 2:45, and all 3 of them will finish a drink at 3:00 for a total of 22.

I'm just sayin' ...

das
Das is correct. JasonF is "semi-correct." His method is rigorously correct ONLY for the LCD intervals in which each preparer has completed an integer number of drinks, in this case 90 s, and 11 drinks completed. Unfortunately, 20 is not an exact multiple of 11, so detail-diving is required.

You can work out a time line:
90 s, Steve , Sue 3, Jack 2, 11 total
120 s, Steve 2, Sue 1, 14 total
135 s, Steve 1, Jack 1, 16 total
150 s, Steve 1, Sue 1, 18 total
165 s. Steve 1, 19 total
180 s, Steve, Sue, Jack each complete drink, 22 total, unles you make two of them stop.

Similar skills are useful in packing shipping containers, as only integer numbers of boxes can be put in (assuming whole shipment is the same product).
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Old 03-12-08, 08:30 AM
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Originally Posted by M2theAX
Just in case here is another one:

x - .20X = 12590


solve for x

Very easy maybe its just late at night and I'm getting tired

x - .20x = 12590
x(1 - .20) =12590
x(.80) = 12590
x = 12590/(.80)
x = 15737.5

Check your answer by plugging in 15737.5 to x.

15737.5 - .20(15737.5) = 12590
15737.5 - 3147.5 = 12590
12590 = 12590
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Old 03-12-08, 08:32 AM
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Originally Posted by das Monkey
The same logic should be applied to that problem. How much water is in a bucket or how many buckets does it take to fill the pool?
das
Exactly. If the number of buckets to fill the pool happens to be a prime number, then it certainly can not be divided by 2, 3, or 6, and in 15 minutes (exactly) none of them will have delivered an exact integer number of buckets.

If the number is divisible by 6, we don't need to know the exact number, only that property, and the 15 minutes is correct.

The lies your teacher your taught you! (it is still a useful approximation, just recognize it isn't exact.)
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Old 03-12-08, 10:53 AM
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Where are they filling their buckets? I can imagine Tony and Sue waiting for Jim to finish filling his bucket the _damn faucet.

"If 1 man can dig a post hole in 20 minutes, 20 men can dig a post hole in 1 minute."

Last edited by Nick Danger; 03-12-08 at 11:02 AM.
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Old 03-12-08, 11:01 AM
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Tony is a lazy mofo if it takes him twice as long to do a job than a girl.
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Old 03-12-08, 11:02 AM
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Originally Posted by OldDude
Das is correct. JasonF is "semi-correct." His method is rigorously correct ONLY for the LCD intervals in which each preparer has completed an integer number of drinks, in this case 90 s, and 11 drinks completed. Unfortunately, 20 is not an exact multiple of 11, so detail-diving is required.

You can work out a time line:
90 s, Steve , Sue 3, Jack 2, 11 total
120 s, Steve 2, Sue 1, 14 total
135 s, Steve 1, Jack 1, 16 total
150 s, Steve 1, Sue 1, 18 total
165 s. Steve 1, 19 total
180 s, Steve, Sue, Jack each complete drink, 22 total, unles you make two of them stop.

Similar skills are useful in packing shipping containers, as only integer numbers of boxes can be put in (assuming whole shipment is the same product).
If this is a computer-graded multiple choice test, there is no provision for detail-diving. They almost certainly want the "flow-rate" answer of 2:44.

You don't get credit for giving the correct real-world answer to a badly formed question.

Interesting problem, though. I would have given Jason's answer, and not thought any further. And I would have been wrong.
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Old 03-12-08, 11:53 AM
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The answer should be the first choice under 2 minutes 44 secs. I worked it out as gven below:

Steve makes each drink in 15 seconds (5 mins = 300 seconds...300/20=15)

Sue makes each drink in 30 secs (10 mins = 600 seconds...600/20= 30)

Jack makes each drink in 45 secs (15 mins = 900 seconds...900/20= 45)


Every 90 seconds they altogether make 11 drinks (6+3+2).

90 divided by 11 = 8.181818181

8.1.8181818181 multiplied by 20 = 163

163 divided into minutes and seconds = 2 mins 44 secs
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Old 03-12-08, 12:32 PM
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Originally Posted by james2025a
The answer should be the first choice under 2 minutes 44 secs.
At 2:44 (164 s), if you work out how many drinks each server has COMPLETED and add them, the total is only 18.
19th drink will be finished by Jack a second later.
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