Capacity - Smallest Container

[Guest]

Two water filters discharge into the same container. Filter A discharges at the rate of 16 quarts per hour and filter B at the rate of 3.5 quarts every 15 minutes. Determine capacity of the smallest container that can be filled in an integral number of minutes by either filter.

Let C = capacity of container.

1 hour = 60 minutes.

Not sure how to proceed.

[Guest]

16 quarts per hour is 4 quarts in 15 minutes
other is 3.5 quarts in 15 minutes
so total is 7.5 in 15 minutes
that is 30 quarts in 1 hour

[Guest]

Determine capacity of the smallest container that can be filled in an integral number of minutes by either filter.

A question:

Could a proportion be used to calculate less than an hour for either?










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Guest

[Guest]

What does this statement mean.....in the context of your question?

"Determine capacity of the smallest container that can be filled in an integral number of minutes by either filter."


What does "integral number of minutes" mean ...??... and what does "by either filter" mean..??.....????

[Guest]

Definition of integral according to Webster:

1."The least whole number; one."

2."Any determinate amount or quantity (as of length, time,
heat, value) adopted as a standard of measurement for
other amounts or quantities of the same kind".

By either filter - My understanding is using either filter to fill the smallest container.

[Guest]

So integral number of minutes ..... really means 1 minute....OR per minute....????

and smallest container.....means the smallest container ever made......?????

eg. 1 milli litre...????......OR 1 spoonfull......OR 1 cubic inch OR 1 cubic millimetre etc

[Guest]

I am assuming per minute and number of quarts by the wording I the problem.

[Guest]

Error in post - should read wording of the problem.

[Guest]

Filter A discharges at the rate of 16 quarts per hour and filter B at the rate of 3.5 quarts every 15 minutes.
Well then the answer is in the question.......The above statement can be written
Filter A discharges at the rate of 16 quarts per 60 minutes and filter B at the rate of 3.5 quarts every 15 minutes.

So Filter A is 16 / 60 = 3.75 quarts per minute
and Filter B is 3.5 / 15 = 0.2333 quarts per minute

[Guest]

Thanks.

[Guest]

Thanks.

I have located another answer:
" 4/15 qt. , 7/10 qt. ; therefore 56/30 qt. or 1 13/15 qt. "

A question - How was that answer obtained ?

[Guest]

Please respond. Thanks.

[Guest]

I have located another answer:
" 4/15 qt. , 7/10 qt. ; therefore 56/30 qt. or 1 13/15 qt. "

A question - How was that answer obtained ?

.....You cannot just pull out answers without a reasonable description and expect others to understand it.

16/60 is same as 4/15 OR 8/30

3.5/15 is same as 7/30

Together adds up to 15/30 same as 1/2 same as 1 quart in 2 minutes .....? ? ? ? ? ? ? ? ? ? ? ? ?

[Guest]

From last post.............
Together adds up to 15/30 same as 1/2 same as 1 quart in 2 minutes .....? ? ? ? ? ? ? ? ? ? ? ? ?
That means 2 minutes to fill a 1 quart container........
OR 1 minute to fill a 1/2 quart container....OR ..... 1 minute to fill 1 pint.....? ? ? ?
but this is from the combined filter outputs added together..........

The question originally asked....
Determine capacity of the smallest container that can be filled in an integral number of minutes by either filter.
So is the answer then......

ERROR......error in earlier post........
So Filter A is 16 / 60 = 3.75 quarts per minute .............this is wrong it is the inverse..???
and Filter B is 3.5 / 15 = 0.2333 quarts per minute ......this is calc OK but not what wanted
It should have read.......
So Filter A is 16 / 60 = 3.75 minutes per quart
and Filter B is 3.5 / 15 = 4.286 minutes per quart
...........................

So to keep both same........per minute.........
So Filter A is 16 / 60 = 0.2667 quarts per minute
and Filter B is 3.5 / 15 = 0.2333 quarts per minute
and add together.......gives 0.5 quarts per minute.....1/2 a quart per minute for both added OR 1 pint per minute

[Guest]

Thanks.

I have re-read the question and the way I understand it means in an integral number of minutes, integral meaning a whole number. The amount could include a fraction or decimal.

[Guest]

.......per minute.........is that not integral or whole number as you state...........
So Filter A is 16 / 60 = 0.2667 quarts per minute
and Filter B is 3.5 / 15 = 0.2333 quarts per minute
and add together.......gives 0.5 quarts per minute.....1/2 a quart per minute for both added OR 1 pint per minute

Why don't you show the working of your answer

[Guest]

I will attempt:

A: 16 quarts per hr. = 16/60 quarts per min. = 8/30 quarts per min.
B: 14 " " " = 14/60 " " " = 7/30 " " "

30 is LCD.


Per minute:

Min. A B

1 8/30 7/30
2 16/30 14/30
3 24/30 21/30
4 32/30 28/30
5 40/30 35/30
6 48/30 42/30
7 56/30 * 49/30
8 64/30 56/30 *
9 72/30 63/30
10 80/30 70/30

* smallest container by both filters.

56/30 = 1 13/15 quarts.

[Guest]

Does this mean in your calculations you are adding A and B...
..............
Per minute:

Min. A B

1 8/30 7/30
..................................

looks like you multiplied the 7 and the 8 to get 56/30 ........what does that mean.? ? ?

if you multiply 8/30 by 7/30 you get 56/900.........but why are you multiplying...? ? ?

[Guest]

I was not multiplying A and B together. I was multiplying the first fractions by each minute. I wasn't sure how to solve.

[Guest]

"Determine capacity of the smallest container that can be filled in an integral number of minutes by either filter."

You wern't sure what you were trying to solve......and I was not sure what you were asking...? ? ?

What you are trying to solve now is the time (whole minutes) that has elapsed for each filter when the amount in quarts that has flowed through each is the same. Then make this the size of the container.

Filter A flows at 8/30 quarts per minute so after 7 minutes 56/30 quarts will have flowed.
Filter B flows at 7/30 quarts per minute so after 8 minutes 56/30 quarts will have flowed
So if make container 56/30 OR 1 and 26/30 quarts then
Container at filter A will fill every 7 minutes
Container at filter B will fill every 8 minutes
and after 56 minutes Filter A container will have filled 8 times ......Total of 8 x 56/30 = 14.9333 quarts
and after 56 minutes Filter B container will have filled 7 times ......Total of 7 x 56/30 = 13.0666 quarts