Antonio, Richard, Miquel and Colin 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.
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Antonio takes 3 minutes, Richard takes 5 minutes, Miquel takes 8 minutes, Colin takes 9 minutes. What is the least amount of time for all four to walk through the tunnel? |
Notes: |
Example:
If Miquel and Colin walk through the tunnel together it will take 9
minutes, If Miquel then walks the torch back through the tunnel a total of 17 minutes will have passed. Continue till all four are at the other end of the tunnel.
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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.
Here is the URL which will take them to Tran Tunnels, a mathematical adventure.
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Michael Stainthorpe Gray, PRU, Oldham
Monday, February 8, 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!
[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.]"
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.
[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
Friday, February 8, 2013
"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,
Monday, February 8, 2016
"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!"