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Working together – practice for Years 8–9

Sample questions on Working together with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 8–9
Curriculum area
Problem solving and non-routine tasks

Question types: Working together

Rule: Working together

If someone does the whole job in 5 hours, they do 1/5 of the job in 1 hour.

Add what they do together in 1 hour; from that you find how long the whole job takes.

Example: 5 h and 20 h: 1/5 + 1/20 = 5/20 = 1/4 of the job per hour → together 4 h

Watch out: Don’t add the times: together it is always faster than the fastest one alone.

Sample questions

  1. Question 1 Easy

    Peter paints 8 m² of fence an hour and Jane paints 8 m². How many hours will it take them together to paint 80 m² of fence?

    Show the solution
    Answer: 5 h

    How it works: 8 + 8 = 16 m²/h; 80 ÷ 16 = 5 h

  2. Question 2 Normal

    One decorator paints a school corridor in 12 hours and another in 36 hours. How many hours will they take working together?

    Show the solution
    Answer: 9 h

    How it works: In 1 h the first does 1/12 of the job and the second 1/36; together 1/12 + 1/36 = 48/432 = 1/9, so 9 h

  3. Question 3 Hard

    One decorator paints a school corridor in 12 hours. With a second decorator helping, they paint it in 9 hours. How many hours would the second decorator take alone?

    Show the solution
    Answer: 36 h

    How it works: In 1 h together they do 1/9 of the job, the first 1/12; the second 1/9 − 1/12 = 3/108 = 1/36, so 36 h

Related topics

All Maths topics

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