Maths Question

[sleeping giant]

My 11 year old came in and asked me the following question and i must admit , i'm stumped :greengrin

If one hose takes 5 minutes to fill a bucket of water , another hose takes 12 minutes to fill the same bucket and another takes 20 minutes to fill the bucket , how quickly would the bucket be filled if all 3 hoses were filling it at the same time ?

Please show your working :greengrin

[Purple & Green]

I assumed the bucket was 60 litres

If the first hose fills it in 5 mins then the flow is 60/5 = 12 litres per min
If the second hose fills it in 12 mins then the flow is 60/12 = 5 litres per min
If the third hose fills it in 20 mins then the flow is 60/20 - 3 litres per min

If you turn them on all together then you would have 12+5+3 litres per min = 20

If the bucket was 60 litres and it's being filled at 20 litres per min, then I think it would be 3 minutes. It's definitely less then five minutes. I think.

[easty]

Could be a load of bollocks but

The first bucket, a, takes 5 mins so 5a=1 and a fills at a rate of 1/5 per min.
The second bucket, b, takes 12 mins so 12b=1 and b fills at a rate of 1/12 per min.
The third bucket, c, takes 20 mins so 20c=1 and c fills at a rate of 1/20 per min.

Lets call the bucket x.

Therefore,
x=5a+12b+20c
x=5(1/5)+12(1/12)+20(1/20)
x=3 mins

[frazeHFC]

"If one hose takes 5 minutes to fill a bucket of water , another hose takes 12 minutes to fill the same bucket and another takes 20 minutes to fill the bucket , how quickly would the bucket be filled if all 3 hoses were filling it at the same time ?"

Assuming it is 60 litres.

5a = 12b = 20c

5a = 60 ------------ a = 12
12b = 60 ---------- b = 5
20c = 60 ----------- c = 3

12 litres per minute, 5 litres per minute, 3 litres per minute.

In 1 minute (12 + 5 + 3 = 20)
In 2 minutes (20 + 20 = 40)
In 3 minutes (40 + 20 = 60)

Answer = 3 minutes

[Sylar]

Could be a load of bollocks but

The first bucket, a, takes 5 mins so 5a=1 and a fills at a rate of 1/5 per min.
The second bucket, b, takes 12 mins so 12b=1 and b fills at a rate of 1/12 per min.
The third bucket, c, takes 20 mins so 20c=1 and c fills at a rate of 1/20 per min.

Lets call the bucket x.

Therefore,
x=5a+12b+20c
x=5(1/5)+12(1/12)+20(1/20)
x=3 mins

That was my approach, rather than trying to define the dimension of the bucket :agree:

[sleeping giant]

I assumed the bucket was 60 litres

If the first hose fills it in 5 mins then the flow is 60/5 = 12 litres per min
If the second hose fills it in 12 mins then the flow is 60/12 = 5 litres per min
If the third hose fills it in 20 mins then the flow is 60/20 - 3 litres per min

If you turn them on all together then you would have 12+5+3 litres per min = 20

If the bucket was 60 litres and it's being filled at 20 litres per min, then I think it would be 3 minutes. It's definitely less then five minutes. I think.

Cheers. This solution is much easier to explain :greengrin

Thanks for everyones input.

[Peevemor]

Cheers. This solution is much easier to explain :greengrin

Thanks for everyones input.

Another way to look at it (which amounts to the same thing) is;


The first hose takes 5 minutes to fill a bucket = 12 buckets/hour
The 2nd hose takes 12 minutes to fill the bucket = 5 buckets/hour
The last takes 20 minutes to fill the bucket = 3 buckets/hour.

Therefore the 3 hoses fill a total of 20 buckets/hour = 1 every 3 minutes. :nerd:

[lapsedhibee]

My 11 year old came in and asked me the following question and i must admit , i'm stumped :greengrin

If one hose takes 5 minutes to fill a bucket of water , another hose takes 12 minutes to fill the same bucket and another takes 20 minutes to fill the bucket , how quickly would the bucket be filled if all 3 hoses were filling it at the same time ?

Please show your working :greengrin

Well now, everyone's saying three minutes BUT BUT BUT the information given in the question is about how long it takes ONE hose to fill a bucket of water. Note specifically the term "the same bucket" - so each hose's performance must have been established in isolation from the other two hoses. Any fule no that if you turn on more than one tap the flow in each tap reduces. Therefore if you have three hoses all filling the bucket at the same time, you won't get the flow in each that you would have got when they were on one at a time.

So I say "More than 3 minutes". :na na:

[Dinkydoo]

Just to chip in, I worked it out as:

In 1 minute,

Hose A has filled 1/5 of the bucket
Hose B has filled 1/12 of the bucket
Hose C has filled 1/20 of the bucket

Standardise the base, so:

Hose A 12/60
Hose B 5/60
Hose C 3/60

Add the fractions together so, In one minute all three hoses running together have filled 20/60 of the bucket - or 1/3.

Multiply by 3 and there you go. 3 minutes.

Edit: just realised I'm a day late with this :doh:

[Future17]

BTW, the answer's 3 minutes.

[danhibees1875]

BODMAS :agree:

[frazeHFC]

BODMAS :agree:

:tee hee:

I remember that arguement, but that BODMASers won! :woohoo: