# Help with figuring out a math formula.

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**1**DVD Talk Special Edition

Thread Starter

Join Date: Apr 2006

Location: New York

Posts: 1,269

**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

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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**2**
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.

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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**8**
Originally Posted by

**M2theAX**The first answer is correct according to them.

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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**9**DVD Talk Special Edition

Thread Starter

Join Date: Apr 2006

Location: New York

Posts: 1,269

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

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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**10**
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

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

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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**11**
The same logic

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

*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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**12**Senior Member

Join Date: Aug 2001

Location: Illinois

Posts: 652

Originally Posted by

**JasonF**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.

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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**13**Senior Member

Join Date: Aug 2001

Location: Illinois

Posts: 652

Originally Posted by

**M2theAX**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 / (3/90 + 2/90 + 1/90)

= 1 / (6/90)

= 90/6

= 15 minutes

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**15**DVD Talk Hero

Join Date: Jul 2001

Location: MI

Posts: 25,043

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

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

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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**16**DVD Talk Ultimate Edition

Join Date: Jul 2001

Location: Lawrence, KS

Posts: 4,284

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

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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**17**DVD Talk Hero

Join Date: Jul 2001

Location: MI

Posts: 25,043

Originally Posted by

**das Monkey**The same logic

das

*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

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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**18**
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."

"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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**20**
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).

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).

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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**21**
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

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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**22**DVD Talk Hero

Join Date: Jul 2001

Location: MI

Posts: 25,043

Originally Posted by

**james2025a**The answer should be the first choice under 2 minutes 44 secs.

19th drink will be finished by Jack a second later.