Annoying question that still gets me at GCSE

Hi guys,

I have this question that has always bugged me and I never quite sussed the method my book was explaining. I got an A at GCSE an I am well into at A-level now, so I thought I would go back and look at it, but it is still getting me. It's a question on ratio and proportion. My algebra is good, so I thought I would look at it with algebra in mind, but I can't get very far with it.

This is an example of a very basic question where I would use algebra. The question goes as follows; 10 boys plan a camp and have sufficient food for 14 days. If 3 boys are ill and cannot go, how long will the food now last?

So I use this method:

10 = k/14

k= 140

7 = 140/y,

7y = 140

y = 140/7 = 20

Now the question I am asking about is a bit bigger.

8 pumps working for 10 minutes raise 440 litres of water. How long will it take 6 pumps to raise 396 litres of water?

I know the answer, but can someone help me with an algebraic method to solve this, please?

Thanks in advance!

Reply 1

TenOfThem

Original post by Tygra

8 pumps working for 10 minutes raise 440 litres of water. How long will it take 6 pumps to raise 396 litres of water?

I know the answer, but can someone help me with an algebraic method to solve this, please?

Thanks in advance!

440 litres needs 80 pump minutes

So 440 = 80k
k = 5.5

396 = 5.5pm

pm = 72

Since p = 6
m = 12

Reply 2

Old_Simon

You doing A level Maths now ?

Reply 3

Tygra

Why do you change 8 to 80 TenofThem?

Also, remember the example question about the boys in the camp and the food? I can set it up like this:

10/7 = y/14

I cross multiply and get 20.

How would you set the question I asked about out in this way??

Reply 4

TenOfThem

Original post by Tygra

Why do you change 8 to 80 TenofThem?

80 pump minutes

8 pumps each at 10 minutes

Reply 5

TenOfThem

Original post by Tygra

How would you set the question I asked about out in this way??

The boys and food are inverse proportion

The litres and pump minutes are direct proportion

Reply 6

Tygra

Original post by Old_Simon

You doing A level Maths now ?

Yes I am.

Reply 7

Old_Simon

Original post by Tygra

Yes I am.

Good luck !

Reply 8

davros

Original post by Tygra

The 80 is in units of "pump minutes" i.e. 8 x 10

Note that you can rewrite your earlier problem in the same way: 10 boys x 14 days gives 140 boy-days' worth of food, so this will last 7 boys 20 days.

Also note that in the pump problem 396 factorizes nicely as 36 x 11 so you can actually do the problem in your head if you're careful since 440/80 = 11/2.

Reply 9

Tygra

Original post by TenOfThem

The boys and food are inverse proportion

The litres and pump minutes are direct proportion

Yes I knew that, I was sking about something else. Don't worry, I've worked it out. Thanks about the 80 pump minute question I asked. Pretty obvious wasn't it?

Reply 10

just george

Another way to look at it logically would be:

8 pumps raises 440 litres in 10 minutes.

you want to raise 396 litres with 6 pumps, so you have 6/8 = 0.75 times as many pumps, and are trying to raise 396/440 = 0.9 times as much water.

So if you think logically less pumps = more time taken, so you divide the 10 minutes by the 0.75; and less water to raise = less time taken, so you multiply the 10 minutes by 0.9.

or in other words the answer would be 10 x (0.9/0.75) = 12 minutes.

Just another way of thinking about it if things like pump minutes etc confuse you, although I'm sure it's not for everyone :smile:

Reply 11

Tygra

Original post by Old_Simon

Good luck !

Thanks, I'm not struggling at all YET. It's strange, I'm finding it easier than I was at the same stage at GCSE. This question I posted was really one of the only things that got me at GCSE.

Reply 12

Tygra

Original post by just george

Ha ha ha ha. That was the way the book explained it. I didn't find it that easy, no offense. I get confused and do things like 8/6 or 440/396.

I'm more comfortable now setting up like this:

80/6x = 440/396

Then solve it with algebra.

Thanks anyway!