Ratio, proportion and percentages

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2.3.1 Try some yourself

Activity 14

A piece of computer software is to be developed by a team of programmers. It is estimated that a team of four people would take a year. Which of the following times is the length of time taken by three programmers?

A 1 year 3 months  B 9 months  C 1 year 4 months

C: 4 programmers take 1 year.

So 1 programmer would take 4 years.

3 programmers would take    years =    or 1 year 4 months.

Activity 15

A 10 kg bag of potatoes lasts for a week when used in catering for 7 people.

• (a) How long will it last for 2 people, assuming everybody eats the same amount?

• (b) If, instead of buying a 10 kg bag (which might not keep well), you want to buy fresh potatoes every week, how much per week should you buy for 2 people?

• (a) First work out how long it would last one person, remembering that it will last longer for one person:

• it lasts 1 week for 7 people, so it lasts 7 weeks for 1 person.

• It will last less than this for 2 people – you need to divide by 2: i.e. it lasts weeks for 2 people.

• (b) You know that in weeks 2 people get through 10 kg of potatoes, so in 1 week 2 people get through 10 ÷   2.86 kg. In practice you would probably buy 3 kg most weeks, and 2 kg when there seemed to be a lot of potatoes left over from the previous week.

Activity 16

Two workers in the Open University warehouse take 20 minutes to stick labels on 500 packages for an MU120 mailing. There are still 4000 more packages. How many workers are required, if the job is to be done in about a further hour?

One worker should take twice as long as two. So 1 worker takes 40 mins for 500 labels. 4000 is 8 times 500 so 1 worker takes 40 × 8 min = 320 mins. 1 hour is 60 mins.

So you need workers .

Practically, you could have 5 workers for = 64 mins (just over an hour) or 6 workers for = 53 mins (just under an hour).

MU120_4M3