Maths questions please

[yoyo123]

I would expect ten year olds to work it out using common multiples, as in G55's explanation. I would encourage them to use a diagram and trial and error to help.

Formal equations would not be taught at that stage, we try to get them to think mathematically and work systematically.

[abhijitc4u]

understood, thanks.

[moved]

I drew boxes for the kennels and wrote the number of dogs. Each time I drew a box for 4 dogs I had an extra empty box to see if it matched the number used for the three dogs and 2 cold dogs.

[yoyo123]

You can't beat a diagram!

[Mum2boys9]

Good afternoon. If anyone could help with this question from Habs maths paper 2013 (I can't ask a tutor as I am diy-ing my son). So any help would be much appreciated x

Q. It takes a team of four people six hours to paint my fence.

How long would a team of eight people have taken? (3hours)

One of my neighbours has a similar fence which is twice as long as mine.
She would like the work to be completed in less than five hours.
What is the minimum number of people that she should emply?

[Guest55]

Q. It takes a team of four people six hours to paint my fence.

How long would a team of eight people have taken? (3hours)

One of my neighbours has a similar fence which is twice as long as mine.
She would like the work to be completed in less than five hours.
What is the minimum number of people that she should emply?

OK - think about how long would one person take - 4 people 6 hours work so how many 'work hours'?

Second part - takes twice as long so how many 'work hours' is that?

I'll post again if these hints don't help.

[Mum2boys9]

Guest55- thank you so much for replying. I am completely confused.
I did initially work out that 1person=12hours? And 12 people do the job in 1.5 hours?
My son and I just cannot work this out. If you do have any more hints, I sincerely would appreciate it. Xx

[Guest55]

Q. It takes a team of four people six hours to paint my fence.

How long would a team of eight people have taken? (3hours)

One of my neighbours has a similar fence which is twice as long as mine.
She would like the work to be completed in less than five hours.
What is the minimum number of people that she should emply?

OK I'll work it through for you - I would call these indirect proportion - in direct proportion more of one variable gives more of the other.

a) I person would take 4 x 6 = 24 hours [needs to do each of the four peoples hours - fewer people take more time]

Eight people would do the work [theoretically] faster than 4 people - so 24/8 = 3 hours

b) The job take 2 x 24 = 48 hours for one person.

We want it done in less than five hours: people x hours = 48 ... can you see the answer?

[Mum2boys9]

my ds said the minimum would be 10? (In 4h 48mins), he continuously divided down, which I think is too lengthy.
I worked out 48h divided by 5, which is 9.6, which I rounded up to 10 people minimum.

Even if we are wrong, being the maths novice I am, I cannot thank you enough for taking the time to explain part of the answer on this forum.

[Guest55]

Yes - I got 10 people by 48/5 and round up as 9 people isn't fast enough.

These are quite tricky as more people links to less time - I've also seen problems about dogs and tins of food, ship crews and supplies etc.