Name: Debbie
Who is asking: Student
Level: All

If you have four people who need to cross a bridge in the dark with only one flashlight and only two of them can cross at a time and their speeds of crossing are as follows:

  • one person can cross it in one minute
  • one person can cross it in two minutes
  • one person can cross it in five minutes
  • and the slowest person can cross it in ten minutes
what is the shortest amount of time it would take to get all four across the bridge?

I figured it to be 19 minutes because the first and second persons would cross together with the flashlight and it would take 2 minutes. It would then take the person who could do it in 1 minute another minute to get back across and get the 5 minuter person. That adds up to 3 minutes. Then they go across in 5 minutes and she has to return for the next person again so one more minute and we're up to 9 minutes. Then the 10 minute and one minute person go across and stay over there because they're all over there now. The total is 19 minutes. But I've been told that is the wrong answer. I cannot figure out what the pattern or formula would be to figure this out. Can you please help???

Hi Debbie,

It seems to me that you want the ten and five minute people to cross together and neither of them to cross again. All the other shuffling back and forth should be done by the one and two minute people. See if you can find a way to do this.



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