Joshua, Matthew, Ethan and Andrew 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.
Joshua takes 2 minutes,
Matthew takes 4 minutes,
Ethan takes 7 minutes,
Andrew takes 9 minutes.
What is the least amount of time for all four to walk through the tunnel?
If Ethan and Andrew walk through the tunnel together it will take 9 minutes, If Ethan then walks the torch back through the tunnel a total of 16 minutes will have passed. Continue till all four are at the other end of the tunnel.
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Joshua and Matthew walk through taking 4 minutes
Joshua walks back with the torch taking 2 minutes [6 minutes total]
Ethan and Andrew walk through taking 9 minutes [15 minutes total]
Matthew walks back with the torch taking 4 minutes [19 minutes total]
Joshua and Matthew walk through taking 4 minutes [23 minutes total]
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