Miquel, Colin, Cody and Alejandro 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.
Miquel takes 3 minutes, Colin takes 4 minutes, Cody takes 6 minutes, Alejandro takes 7 minutes. What is the least amount of time for all four to walk through the tunnel? 
Notes: 
Example:
If Cody and Alejandro walk through the tunnel together it will take 7
minutes, If Cody then walks the torch back through the tunnel a total of 13 minutes will have passed. Continue till all four are at the other end of the tunnel.
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Topics: Starter  Logic  Problem Solving  Puzzles
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Previous Day  This starter is for 8 February  Next Day
22 minutes:
Miquel and Colin walk through taking 4 minutes
Miquel walks back with the torch taking 3 minutes [7 minutes total]
Cody and Alejandro walk through taking 7 minutes [14 minutes total]
Colin walks back with the torch taking 4 minutes [18 minutes total]
Miquel and Colin walk through taking 4 minutes [22 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.
Teacher, do your students have
access to computers? 

Here a concise URL for a version of this page without the comments.
Transum.org/go/?Start=February8
Here is the URL which will take them to Tran Tunnels, a mathematical adventure.