River Crossing
Problem
Four people, A, B, C and D need to get across a river. The only way to cross the river isby an old bridge, which holds at most 2 people at a time. Being dark, they can't cross thebridge without a torch, of which they only have one. So each pair can only walk at thespeed of the slower person. They need to get all of them across to the other side as quickly as possible. A is the slowest and takes 10 minutes to cross; B takes 5 minutes; Сtakes 2 minutes; and D takes 1 minute.
What is the minimum time to get all of them across to the other side?
Hints
Hint 1
A and B should go together
Solution
Show Solution
17 minutes
Show Explanation
To utilize the event that A and B go together to optimize time. The routine is as below:
- C and D cross together in 2 minutes.
- D returns with the flashlight in 1 minute.
- A and B cross together in 10 minutes.
- C returns with the flashlight in 2 minutes.
- C and D cross together again in 2 minutes.
Total: 2 + 1 + 10 + 2 + 2 = 17 minutes