**Inverse Proportion**

Starter

It is known that with 4 workers the mean average time taken complete a job schedule is 30 minutes.

A company has 8 workers working a shift.

Their boss says "we have twice the number of workers, so it is going to take about double the time, guess we have hard hours work ahead of us".

Explain why the boss is wrong, what is mistake he has made, and how long it should take to complete the job schedule.

Inverse Proportion

Workers Time taken

4 30 minutes

8 15 minutes

12 minutes

20 minutes

2 minutes

1 minutes

Inverse proportion

In the starter, when there were double the number of people, it took half the time.

What do you think would happen if we had three times the number of people?

5 times the number of people?

**L.O. - To recognise what it means for two**

quantities to be inversely proportional, and

how we represent inversely proportional

relationships.

quantities to be inversely proportional, and

how we represent inversely proportional

relationships.

Starter

It is known that with 4 workers the mean average time taken complete a job schedule is 30 minutes.

A company has 8 workers working a shift.

Their boss says "we have twice the number of workers, so it is going to take about double the time, guess we have hard hours work ahead of us".

Explain why the boss is wrong, what is mistake he has made, and how long it should take to complete the job schedule.

The boss is wrong because the time taken to complete the jobs should go down not up.

He mistakenly thinks that the number of workers and the time taken to complete jobs is in proportion - i.e. double the jobs and double the time taken.

In reality with double the number of workers, it should take half the time, so about 15 minutes.

What numbers would go in the spaces?

How can we represent the relationship

between the number of workers and the

time taken?

Inverse Proportion

Workers Time taken

4 30 minutes

8 15 minutes

12

10

minutes

20

6

minutes

2

60

minutes

1

120

minutes

What numbers would go in the spaces?

How can we represent the relationship

between the number of workers and the

time taken?

Time taken = 120/number of workers

OR

Time take x number of workers = 120

Inverse Proportion

Pushing a block of mass 30 kg causes an acceleration of 5 ms .

What would the acceleration be on a 20 kg object?

What are we assuming here?

-2

Inverse Proportion

Pushing a block of mass 30 kg causes an acceleration of 5 ms .

What would the acceleration be on a 20 kg object?

30 x 5 = 150. 150/20 = 7.5 ms

OR ratio of masses = 30:20 so ratio of accelerations must be ?:5. 20/4 = 5 so 30/4 = 7.5 ms

What are we assuming here?

-2

-2

-2

That we push with the same Force.

Main Activity 1

Complete the RAG sheet on Inverse

Proportion.

Main Activity 1 Answers

Red:

(a) I is halved (becomes 0.25).

(b) I = 0.33333 (or )

1

3

1)

2) (a) The volume is halved (becomes 4 litres)

(b) The volume is quartered (becomes 2 litres)

(c) 80 Nm

3) (a) 425 Hz

(b) 0.4 m

-2

Amber:

4) (a) 3.5

(b) Would have increased to 14.

5) (a) Yes - 3 x 8000 = 4 x 6000 = £24000

(b) (i) £2400 (ii) after 24 years.

Plenary

Exam question challenge

Which groups can answer the exam question together?

Plenary Worked Answers

(a) 800 letters

(b) It would take 4 people 2.5 hours to stuff 1000 envelopes. It would therefore take 1 person 10 hours and so 5 peop could do it in 2 hours. This means it takes 4 people 30 minutes more than 5 people.

(c) Sam's assumption is not reasonable because people cannot work at the same rate without a break for 12 hours.

Assuming this means that Sam's answer of 7200 is larger than the actual number of letters that 3 people could put into envelopes in a day.

**Key**

Examples

Examples

**Worked**

example

example

**Worked**

example

example

**Activities**

**Activity**

Answers

Answers