Joseph, William, David and Nicholas have to walk through a long dark tunnel. They only have one torch between them so a maximum of two people can go through the tunnel at any one time. Each person takes a different amount of time to get through the tunnel and if two people walk together they must walk at the rate of the slowest.
Joseph takes 3 minutes,
William takes 5 minutes,
David takes 8 minutes,
Nicholas takes 11 minutes.
What is the least amount of time for all four to walk through the tunnel?
If David and Nicholas walk through the tunnel together it will take 11 minutes, If David then walks the torch back through the tunnel a total of 19 minutes will have passed. Continue till all four are at the other end of the tunnel.
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Joseph and William walk through taking 5 minutes
Joseph walks back with the torch taking 3 minutes [8 minutes total]
David and Nicholas walk through taking 11 minutes [19 minutes total]
William walks back with the torch taking 5 minutes [24 minutes total]
Joseph and William walk through taking 5 minutes [29 minutes total]
Note to teacher: Doing this activity once with a class helps students develop strategies. It is only when they do this activity a second time that they will have the opportunity to practise those strategies. That is when the learning is consolidated. Click the button above to regenerate another version of this starter with different numbers and names.
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Teacher, do your students have
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