Help them!

Sultan · 2014-04-08 05:00:28

Hi guys,
This's my first post in this great forum.
Today, i have something to share you with.
It's a puzzle which came out of the blue when i was working on my homework
It's quite looong but it does make sense (i guess )
Here you go guys>>

A factory produces chemical liquids in special flasks with special lids.

This factory will produce:
> 99 flasks numbered from 1 to 99
> 99 chemical liquids numbered from 1 to 99 Each liquid has a distinctive color.
> The time required to fill a flask with a single chemical liquid= 1 minute.
> The time required to empty that flask = 0.5 minute.

>> two workers will fill the 99 flasks with the chemical liquids (carefully) pursuant to numbers. (Liquid no.1 in flask no. 1 and liquid no. 2 in flask no. 2, and so on)

>> After filling all 99 flasks, a special machine will start closing the flasks with lids. (This machine starts at a predetermined time can not be amended except by the supervisor).

>> When the 2 workers had finished filling all 99 flasks they realized that the flasks have been numbered wrongly! (meaning the flask that is supposed to be No. 1 has been given No.99 and the flask that is supposed to be No. 2 has been given No. 98, and so on).
They decided to refill them again in reverse order to pour every liquid in the designated flask!
Note: the two workers can't empty or refill same flask at a time.

The DILEMMA is that after 74 minutes, the 99 flasks should be filled and placed in the designated area (under the machine) to start closing the flasks with the lids AND the supervisor has left the factory!
Note: ignore the time needed to carry the flasks from the filling area to lids closing area!

The question is: Are the 74 minutes sufficient to accomplish the task (empty and refill again) and put the flasks in the designated area before the machine starts working, and
What is the minimum time in which they can finish the task?

Will the workers be able to avoid the factory squandering high-cost lids if the machine started working before placing the flasks, as well as delay shipment schedule, which as a whole may be a compelling reason to fire the 2 workers

Waiting for any smart answer

Last edited by Sultan (2014-04-14 10:28:09)

phrontister · 2014-04-08 15:38:11

Hi, and welcome to the forum!

I haven't got anywhere with this yet, but before I look at it more closely I'd to know:
- if the task of filling/emptying a flask requires both workers, and
- if they (either together or alone) can only fill/empty one flask at a time.

If the answers to these questions are "no", then the workers may find it handy to utilise holding a flask in each hand for something or other.

Also, I take it that the flasks don't need to be sterilised between fills.

Last edited by phrontister (2014-04-14 02:25:37)

Sultan · 2014-04-12 12:06:13

Hi phrontister,

- No
- No

The worker can not do 2 tasks at the same time ( holding 2 flasks in each hand is doing 2 tasks at a time!)

Don't worry the liquid itself is steriliser;)

phrontister · 2014-04-13 04:05:22

Hi Sultan,

"Yes", to all three questions.

The question is: Are the 74 minutes sufficient to accomplish the task (empty and refill again) and put the flasks in the designated area before the machine starts working

Answer: More than sufficient. In fact, with the two workers emptying and refilling their respective flasks at exactly the same rate as each other and working as quickly as they did, they had time to take a 15-second 'breather' together after each fill and still had 15 seconds to go before the machine would start working.

But they were experienced workers and knew beforehand exactly how long it would take them, and that by taking those short breaks they'd be able to maintain their energy levels right through to the end and finish as fresh as daisies , instead of maybe flagging in the home straight and failing to beat the clock! >puff-puff<

Last edited by phrontister (2014-04-13 12:35:58)

Sultan · 2014-04-13 12:48:21

Hi phrontister,

Great!
But how long it will take them to do this task?! (The minimum time in minutes)

phrontister · 2014-04-13 14:16:51

Hi Sultan,

But how long it will take them to do this task?!

Last edited by phrontister (2014-04-13 14:18:32)

Sultan · 2014-04-15 23:48:54

Hi phrontister,

I'm afraid your answer isn't accurate
It might be because the way you understood the puzzle!
Can you explain how you got it

phrontister · 2014-04-16 01:43:58

Hi Sultan,

O...I was hoping I was right.

Last edited by phrontister (2014-04-21 21:41:41)

Agnishom · 2014-04-21 15:08:20

In ancient Persia, there lived a Sultan whose only daughter was as beautiful as moonrise in clear heaven.

Hi sultan,

how is the princess doing?

Sultan · 2014-05-04 05:02:00

Hi Agnishom
she is yearningly waiting for the knight who can defeat the puzzle:D

ManiticMath · 2014-05-12 04:55:15

I don't understand why they don't just put new labels on them in the correct order. they would need new containers to put them into due to the fact that now bottle #1 is contaminated with liquid #99, So they would either have to decomtaminate the flasks, or bottle them in new bottles, or just relabel them.

Math Is Fun Forum

#1 2014-04-08 05:00:28

Help them!

#2 2014-04-08 15:38:11

Re: Help them!

#3 2014-04-12 12:06:13

Re: Help them!

#4 2014-04-13 04:05:22

Re: Help them!

#5 2014-04-13 12:48:21

Re: Help them!

#6 2014-04-13 14:16:51

Re: Help them!

#7 2014-04-15 23:48:54

Re: Help them!

#8 2014-04-16 01:43:58

Re: Help them!

#9 2014-04-21 15:08:20

Re: Help them!

#10 2014-05-04 05:02:00

Re: Help them!

#11 2014-05-12 04:55:15

Re: Help them!

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