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?
Answers
Answer:
The minimum value of x is just 30 mins .
Step-by-step explanation:
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 -
Person 1 - One minute
Person 2 - 4 mins
Person 3 - 8 mins
Person 4 - 15 mins .
When two people cross the bridge together (sharing the flashlight), they both walk at the slower person’s pace.
Solution
The shortest strategy is -
Person 1 and person 2 go together. They will take 4 mins to reach the other side of the bridge. Then person 1 returns.
Now person 1 goes with person 3 , taking 8 mins .
Then person 1 again returns .
Finally person 1 goes with person 4 taking 15 mins .
Total time taken ( In mins )
> 4 + 1 + 8 + 1 + 15
> 29 mins.
The safest value of x is 30 mins . This is the required answer.
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Answer:
Given :-
- 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 minutes 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.
To Find :-
- What is the minimum value of x.
Solution :-
Given that :
★ People A ------------------- 1 minutes
★ People B ------------------- 4 minutes
★ People C ------------------- 8 minutes
★ People D ------------------- 15 minutes
➦ First time, People A and People B cross the bridge, so the time taken for this is 4 minutes.
➦ Now, People A will go back, so the time taken for this is 1 minutes.
➦ Now, People A will give the flashlight to People C and People C and People D will cross the bridge, so the time taken for this is 15 minutes.
➦ Again, People C will give the flashlight to People B and People B will come back for 4 minutes.
➦ Now, People A and People B will cross the bridge, so the time taken for this is 4 minutes.
Hence, we can draw :
➲ People A & People B ➔ 4 minutes to go.
➲ People A ➔ 1 minutes to go back.
➲ People C & People D ➔ 15 minutes to go.
➲ People B ➔ 4 minutes to come back.
➲ People A & People B ➔ 4 minutes to go.
Hence, the required time taken is :
↦ Required time taken = 4 minutes + 1 minutes + 15 minutes + 4 minutes + 4 minutes
↦ Required time taken = 5 minutes + 15 minutes + 4 minutes + 4 minutes
↦ Required time taken = 20 minutes + 4 minutes + 4 minutes
↦ Required time taken = 24 minutes + 4 minutes
➠ Required time taken = 28 minutes
∴ The minimum value of x is 30 minutes.