Inverse proportion

The Maths Habit

More workers, less time.
When else does more of
one thing mean less
of another?

Faster speed, shorter journey

More people sharing, smaller share

More taps, less time to fill

Inverse proportion
When one amount is multiplied, the other is divided by the same number.

3 workers paint a hall in 8 hours. Each block is one worker for one hour. How many blocks of work is the job?

3 workers8 hours

3 × 8 = 24 blocks

4 workers share the same 24 blocks. How many hours does it take?

4 workers6 hours

24 ÷ 4 = 6 hours

More workers, fewer hours: workers × hours stays 24

WorkersHours 212 46

A journey takes 4 hours at 30 mph.

Speed (mph)30601540
Time (hours)4

It takes 6 workers 4 hours to dig a trench. How long would it take 8 workers? 3 hours

It takes 5 workers 6 hours to tile a floor. How long would it take 3 workers? 10 hours

It takes 6 workers 4 hours to dig a trench. How long would it take 8 workers? 3 hours

It takes 4 workers 9 hours to build a wall. How long would it take 6 workers? 6 hours

It takes 6 workers 4 hours to dig a trench. How long would it take 8 workers? 3 hours

It takes 2 pumps 15 hours to empty a pond. How long would it take 5 pumps? 6 hours

It takes 6 workers 4 hours to dig a trench. How long would it take 8 workers? 3 hours

It takes 9 friends 2 hours to tidy a garden. How long would it take 3 friends? 6 hours

It takes 6 workers 4 hours to dig a trench. How long would it take 8 workers? 3 hours

It takes 8 people 3 hours to pick the apples in an orchard. How many people would pick them in 2 hours? 12 people

Inverse proportion worksheet, page 1

Inverse proportion worksheet, page 2

Answer sheet

  1. A car drives 3 hours at 50 mph. The journey back takes 2.5 hours. What was its speed on the way back?

    60 mph
  2. 12 painters can paint a school in 10 days. After 4 days, 4 painters leave. How many more days will it take?

    9 days

  1. 6 workers take 10 hours to lay a patio. How long would 4 workers take?

    15 hours
  2. A trip takes 3 hours at 40 mph. How long does it take at 60 mph?

    2 hours
  3. 3 taps fill a pool in 8 hours. Ravi says 6 taps would take 16 hours. Is he right? Explain.

    No: 4 hours, more taps take less time
Exit tickets to print