Transum Tunnel

A Maths Starter of The Day

Daniel, Anthony, Christopher and Joseph 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.
Transum Tunnel

Daniel takes 2 minutes to walk through,
Anthony takes 5 minutes to walk through,
Christopher takes 9 minutes to walk through,
Joseph takes 10 minutes to walk through.

What is the least amount of time for all four to walk through the tunnel?

Notes:
1. All four begin at the same end of the tunnel.
2. The torch must be walked back through the tunnel by at least one person, it cannot be thrown.
3. The answer is less than 28 minutes!

Example:
If Christopher and Joseph walk through the tunnel together it will take 10 minutes, If Christopher 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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Keywords: Starter | Logic

  • Claudia Walters, St Mary's High
  • Wednesday, February 07, 2007
  • "These resources are excellent
    Thank you
    Can you recommend any practical resource sites for non-whiteboard resources?"
  • Mounts Bay School, Top Set Year 7
  • Friday, February 08, 2008
  • "Hard but satisfying."
  • Matt Wallace, Hopewell, Pa
  • Tuesday, February 03, 2009
  • "Wow! That was great!!! you definitely had to think outside of the box on that one! "
  • Michael Stainthorpe Gray, PRU, Oldham
  • Monday, February 08, 2010
  • "The first time we looked at the Transum Tunnel problem it had different number of minutes/names etc What has happened to them we need to check the answer!"

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This starter has scored a mean of 3.9 out of 5 based on 42 votes.

 

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ANSWER

27 minutes:

Daniel and Anthony walk through taking 5 minutes
Daniel walks back with the torch taking 2 minutes [7 minutes total]
Christopher and Joseph walk through taking 10 minutes [17 minutes total]
Anthony walks back with the torch taking 5 minutes [22 minutes total]
Daniel and Anthony walk through taking 5 minutes [27 minutes total]
Computer Teacher, do your students have access to computers?
Do you have "Laptops in Lessons"?

Whether your students each have a TabletPC or share a desktop PC, this activity lends itself to eLearning (Engaged Learning).

Laptop

Here's the URL which will take
them to Tran Tunnels, a mathematical adventure.

http://www.transum.org/go/?to=Tunnels