Any mathematicians out there??

max888

Does anybody want to have a crack at an algebraic puzzle, I have not got very far i.e. nowhere at all.

'A small swimming pool can be filled with two pipes in 3 hours. If the larger pipe alone takes 8 hours less than the smaller pipe to fill the pool, find the time in which it will be filled by each pipe singly.'

Thanks,

Max

nolf

I'm struggling with that.

Large pipe must be more than 3 hours, so small pipe must be more than 11.

And I can't get further than that.

max888

Thanks for your help it's further than I got, I'll just keep going back to it.

Max

nolf

Got it.

PMed.

RichN95.

12 hours and 4 hours.

Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

Therefore 300/3=X+Y. So X=100-Y

And 300/X - 8 = 300/Y

Multiply by X and Y: 300Y -8XY= 300X

Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

Simplify: Y^2 -25Y -3,750 = 0

Solve : Y= 75 so X=25

Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

Flasheart

RichN95 wrote:

12 hours and 4 hours.

Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

Therefore 300/3=X+Y. So X=100-Y

And 300/X - 8 = 300/Y

Multiply by X and Y: 300Y -8XY= 300X

Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

Simplify: Y^2 -25Y -3,750 = 0

Solve : Y= 75 so X=25

Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

:shock: :shock: :? :? :oops: :oops:

I is fick :oops:

nolf

Same as I got, but different. I put pool full = 1 and solved it like:

Pool Full = 1 (arbitrarily)

large pipe time alone = x
small pipe time alone = y,
y = x+8

3 hours is the total time so you divide it by the individual pipes to get their contribution.

(3/x+8 ) + (3/x) = 1

times by x(x+8 ) gives

3x + 3(x+8 )l = x(x+8 )

3x + 3x+24= x^2 + 8x
(-6x, - 24) equals

0 = x^2 + 8x - 6x - 24
0 = x^2 + 2x - 24

0 = (x-4)(x+6)

only positive answer is that x (large pipe) = 4
therefore y (small pipe) = x+8 = 12.

RichN95.

nolf wrote:

Same as I got, but different. I put pool full = 1 and solved it like:

The maths is essentially the same though.

softlad

you lot need to get out more....

max888

Thanks everyone for your help, it's much appreciated!

mrushton

Good to know that 32 years after leaving school I am still 5H1T at algebra. X? Y? Why? I work at a Uni and sometimes I see equations on a board and the rabble studying them and think how smart they are. Recently had a Nuclear Technology Conference at the Uni and all of the Ph. D students were ridiculously smart. It prob.was akin to rocket science.

wheezee

Did you lot just do Max's homework for him?

angry_bird

Umm i just sort of figured it straight away (without looking at the other answers) quite by accident i think, it sort of clicked :oops: I was always crap a algebra at school, i just didn't like the look of it... god knows what you guys have written up there but it just confuses me, thank god i decided not to bother studying physics at uni...

Matt the Tester

Flasheart wrote:

RichN95 wrote:

12 hours and 4 hours.

Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

Therefore 300/3=X+Y. So X=100-Y

And 300/X - 8 = 300/Y

Multiply by X and Y: 300Y -8XY= 300X

Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

Simplify: Y^2 -25Y -3,750 = 0

Solve : Y= 75 so X=25

Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

:shock: :shock: :? :? :oops: :oops:

I is fick :oops:

i feel the same way!

nolf

Here's some more fun questions:

Pool filled in 3 hours (originally), than a leak appeared!!

If full, the pool completely empties in 5 hours through the annoying leak.

How long does the pool take to fill, bearing in mind the annoying leak?

Turbo Man

nolf wrote:

Here's some more fun questions:

Pool filled in 3 hours (originally), than a leak appeared!!

If full, the pool completely empties in 5 hours through the annoying leak.

How long does the pool take to fill, bearing in mind the annoying leak?

9 hours

Edit - no, 7.5 hours ...

max888

Did you lot just do Max's homework for him

It's not technically homework, just a small pack to stop me forgetting everything over the holidays!

Splottboy

Plug the hole or buy a new pool?!

garrynolan

Assume it fills at 100 gals per hour, pool holds 300 gals. 5 hours to empty = 300 divided by 5 = 60 gals per hour lost; ergo pools fills at 100 - 60 = 40 gals per hour. Filling 300 gal pool @ 40 gals per hour = 7hours 30mins. Don't ask me how to do this using 'proper' algebra as I wouldn't have a clue!
By the way... can someone explain in layman's language how binary works? In 1st year at Secondary I was a lazy git so got kicked out of the top class into the next one down - they had already done binary, we hadn't, so I missed it. There was a question on my O-level paper using binary and I couldn't even attempt it. Ta.

RichN95.

steady rider wrote:

Flasheart wrote:

RichN95 wrote:

12 hours and 4 hours.

Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

Therefore 300/3=X+Y. So X=100-Y

And 300/X - 8 = 300/Y

Multiply by X and Y: 300Y -8XY= 300X

Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

Simplify: Y^2 -25Y -3,750 = 0

Solve : Y= 75 so X=25

Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

:shock: :shock: :? :? :oops: :oops:

I is fick :oops:

i feel the same way!

We all show thickness in different ways. I didn't realise it was a bank holiday until they mentioned it on the radio at 8.30 on Monday morning. Now that's thick.

Weejie54

What if it's raining?

This looks interesting...

Frank the tank

Oi!!!!!!!! VORDERMAN I said NOOOOOOOOOOOOOOOOOOO.

Matt the Tester

RichN95 wrote:

steady rider wrote:

Flasheart wrote:

RichN95 wrote:

12 hours and 4 hours.

Make the pool 300 units in size. Make the rates of the two pipes X and Y units per hour. (Y is the faster)

Therefore 300/3=X+Y. So X=100-Y

And 300/X - 8 = 300/Y

Multiply by X and Y: 300Y -8XY= 300X

Substitute X: 300Y -800Y +8Y^2 = 30,000 -300Y

Simplify: Y^2 -25Y -3,750 = 0

Solve : Y= 75 so X=25

Therefore times are 300/75 and 300/25. 8 hours and 4 hours.

:shock: :shock: :? :? :oops: :oops:

I is fick :oops:

i feel the same way!

We all show thickness in different ways. I didn't realise it was a bank holiday until they mentioned it on the radio at 8.30 on Monday morning. Now that's thick.

no i think thats ignorance at it's best

max888

no i think thats ignorance at it's best

as they say "ignorance is bliss"

Bunneh

I'm terrible at mathematics but I'm exceptional at working with my hands (shut up Flasheart ). The first day at secondary school they gave us algebra, I'd never done it before and being the quiet lad I was back then I didn't ask. Spent my entire time at school struggling with maths with no one even helping me. The kids in the low sets were ignored and given up on, whilst the kids in high sets were encouraged.

max888

It not that like at my school. Last year I was in the second lowest set but got an A* at IGCSE. Everyone gets really good support and the teaching is excellent!

bompington

Max888 wrote:

It not that like at my school. Last year I was in the second lowest set but got an A* at IGCSE. Everyone gets really good support and the teaching is excellent!

@Max888's teacher - come on now, we all know it's easy to hack your kids' online accounts, but it's really unprofessional to use them!

max888

No hacking going on here but no sh1t, at my last school I could not do any maths at all but hey I just got top marks at GCSE, I ain't complaining.

Bunneh

Bear in mind my experiences are from the late 80s to early 90s. Thing have changed somewhat and I have done quite a good number of courses, from English through to my European Computer Driving License (chocolate teapot?). You get support, and good tutors who actually do give a damn - I seem to recall my Maths teacher giving up and my English teacher whining that my stories were too imaginative. I suspect she couldn't be arsed reading 12 pages...

beverick

mrushton wrote:

Good to know that 32 years after leaving school I am still 5H1T at algebra. X? Y? Why? I work at a Uni and sometimes I see equations on a board and the rabble studying them and think how smart they are. Recently had a Nuclear Technology Conference at the Uni and all of the Ph. D students were ridiculously smart. It prob.was akin to rocket science.

Good to know that 31 years after leaving school, and having to learn sufficient algebra to pass various science exams, that I still don't understand it, I still can't do it and, what's more, during my entire working life I've never needed to.

Bob

nolf

Turbo Man wrote:

nolf wrote:

Here's some more fun questions:

Pool filled in 3 hours (originally), than a leak appeared!!

If full, the pool completely empties in 5 hours through the annoying leak.

How long does the pool take to fill, bearing in mind the annoying leak?

9 hours

Edit - no, 7.5 hours ...

2nd one is right.