Katherine, Alexandra, Rachel and Lily 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.
Katherine takes 2 minutes,
Alexandra takes 3 minutes,
Rachel takes 5 minutes,
Lily takes 7 minutes.
What is the least amount of time for all four to walk through the tunnel?
If Rachel and Lily walk through the tunnel together it will take 7 minutes, If Rachel then walks the torch back through the tunnel a total of 12 minutes will have passed. Continue till all four are at the other end of the tunnel.
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Katherine and Alexandra walk through taking 3 minutes
Katherine walks back with the torch taking 2 minutes [5 minutes total]
Rachel and Lily walk through taking 7 minutes [12 minutes total]
Alexandra walks back with the torch taking 3 minutes [15 minutes total]
Katherine and Alexandra walk through taking 3 minutes [18 minutes total]
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