Four people are on this side of the bridge. The bridge will be destroyed by a bomb in x minutes. Everyone has to get across before that. Problem is that it’s dark and so you can’t cross the bridge without a flashlight and they only have one flashlight. Plus the bridge is only big enough for two people to cross at once. The four people walk at different speeds: one fellow is so fast it only takes him 1 minute to cross the bridge, another 4 minutes, a third 8 minutes, the last it takes 15 minutes to cross the bridge. When two people cross the bridge together (sharing the flashlight), they both walk at the slower person’s pace. If they all get across before the bridge blows up then find out the minimum value of x?
Solution: Suppose person A takes 1 minute, B takes 4 minutes, C takes 8 minutes and D takes 15 minutes to cross the bridge.
First time A and B cross the bridge so the time taken for this is 4 minutes.
Now A will go back so the time taken for it will be 1 minute.
Now A will give the battery to C and C and D will cross the bridge so the time taken for it will be 15 minutes.
Then C will give the battery to B and B will come back for 4 minutes.
Now A and B will cross the bridge so the time taken for it will be 4 minutes.
So the total time taken is = 4 + 1 + 15 +4 + 4 =28 minutes.
1.——– A & B——— 4 minutes(go)