Transum Tunnel

A Maths Starter of The Day

Riley, Sofia, Haley and Gabrielle 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

Riley takes 2 minutes to walk through,
Sofia takes 5 minutes to walk through,
Haley takes 9 minutes to walk through,
Gabrielle takes 12 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 30 minutes!

Example:
If Haley and Gabrielle walk through the tunnel together it will take 12 minutes, If Haley then walks the torch back through the tunnel a total of 21 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!"
  • Marry Singilton, Mount Cook School
  • Tuesday, February 08, 2011
  • "WOW Amazing a good use of 30min."

    •  

  • Lauren And Year 9, Cramlington Learning Village
  • Monday, February 14, 2011
  • "This is a good question but we would like to know the answer because we are not quite sure."

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This starter has scored a mean of 3.8 out of 5 based on 77 votes.

 

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ANSWER

29 minutes:

Riley and Sofia walk through taking 5 minutes
Riley walks back with the torch taking 2 minutes [7 minutes total]
Haley and Gabrielle walk through taking 12 minutes [19 minutes total]
Sofia walks back with the torch taking 5 minutes [24 minutes total]
Riley and Sofia walk through taking 5 minutes [29 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 is the URL which will take them to a concise version of this page.

Transum.org/go/?Start=February8

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

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