Transum Tunnel

A Maths Starter of The Day

Madison, Abigail, Olivia and Isabella 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

Madison takes 3 minutes to walk through,
Abigail takes 5 minutes to walk through,
Olivia takes 8 minutes to walk through,
Isabella 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 29 minutes!

Example:
If Olivia and Isabella walk through the tunnel together it will take 10 minutes, If Olivia then walks the torch back through the tunnel a total of 18 minutes will have passed. Continue till all four are at the other end of the tunnel.

 

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  • 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! "

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This starter has scored a mean of 3.9 out of 5 based on 41 votes.
 

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ANSWER

28 minutes:

Madison and Abigail walk through taking 5 minutes
Madison walks back with the torch taking 3 minutes [8 minutes total]
Olivia and Isabella walk through taking 10 minutes [18 minutes total]
Abigail walks back with the torch taking 5 minutes [23 minutes total]
Madison and Abigail walk through taking 5 minutes [28 minutes total]
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).

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

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