Ashley, Sophia, Elizabeth and Alexis 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.

 Ashley takes 2 minutes, Sophia takes 5 minutes, Elizabeth takes 9 minutes, Alexis takes 12 minutes. 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 Elizabeth and Alexis walk through the tunnel together it will take 12 minutes, If Elizabeth 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.

Topics: Starter | Logic | Problem Solving | Puzzles

• Claudia Walters, St Mary's High
•
• These resources are excellent
Thank you
Can you recommend any practical resource sites for non-whiteboard resources?

[Transum: Have a look at the iPad Maths page.]
• Mounts Bay School, Top Set Year 7
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• Hard but satisfying.
• Matt Wallace, Hopewell, Pa
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• Wow! That was great!!! you definitely had to think outside of the box on that one!
• Michael Stainthorpe Gray, PRU, Oldham
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• 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!

[Transum: Sorry Michael, it is a feature of most of the Transum pages that each time the page is loaded a different version of the puzzle or problem is generated. This is so that if pupils are working from their own computers they are trying to answer different versions of the same question. This encourages discussions about method rather than the sharing of answers. This feature also allows you to revisit a Starter on another occasion and try to solve it again with different numbers involved.]
• Marry Singilton, Mount Cook School
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• WOW Amazing a good use of 30min.
• Lauren And Year 9, Cramlington Learning Village
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• This is a good question but we would like to know the answer because we are not quite sure.

[Transum: The answers to Transum Starters and other activities are available to subscribers. Scroll down this page to find the links.]
• Class 1 Year 6, Brentwood Prep
•
• We calculated that it took 26 mins. Lucas and Juan start and take 13 mins. As soon as they finish Juan comes back shining the torch whilst Aaron starts from the other end at the same time, he takes 8 mins. When he is over the last 2 set off, Juan and Charles together taking 5 mins. 13+8+5=26 mins. It does not say that you cannot walk without a torch as long as there are only 2 people in the tunnel at one time.
• Transum,
•
• It's a great puzzle isn't it? Regarding the comments above, each time this page is loaded the names of the people change and the times change too so if you want to know the answer (subscribers only) make sure you scroll down the page before reloading it!

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

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

Transum.org/go/?to=tunnels

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