Painting a fence Dragan painting the fence in 2 hours. Patric make it in 4 hours. How long will it take if they help each other – i.e. they both paint.

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Presentation transcript:

Painting a fence Dragan painting the fence in 2 hours. Patric make it in 4 hours. How long will it take if they help each other – i.e. they both paint at the fence at the same time? Try to solve the problem in many different ways.

Painting a fence This is a type of mathematical problem that has been around for at least 2500 years – it is sometimes called the “time problem”.

Painting a fence 1. It only take a third of the time if they help each other compared to if Patric should paint it by himself. i.e. 1/3 of 4 hours is 4/3 = 1 1/3 h = 1 h, 20 min Dragan Patric

Painting a fence 2. In 1 hour Dragan is painting half of the fence. At the same time Patric painting 1/4 of the fence. Then there is 1/4 of the fence left. If the help each other with this part, Dragan is painting 2/3 of it and Patric 1/3 of it. DraganPatric DraganDr PaPatric

Painting a fence Patric is painting 1/4 of the fence in 1 hour. But now he is painting 1/3 of 1/4. That must take 1/3 of a hour and that is 20 minutes. Totally it takes 1 hour and 20 minutes.

Painting a fence 3. In 4 hours, Dragan and Patric should paint 3 fences – i.e. they should paint one fence in 1/3 of that time. 4/3 h = 1 h, 20 min Time (h)1234 Dragan½11 ½2 Patric¼½¾1 Sum3

Painting a fence 4. With equation It takes them x hours to paint the fence together.