The goal is to get four people across a town in 17 minutes using a car that can hold two people. The times taken by each person to pass the town are 1, 2, 5, and 10 minutes. We need to minimize the total time taken.
To minimize the total time, the fastest individuals should be utilized for returning the car to pick up the remaining people, as this will save time.
The first trip should include the two fastest individuals (1 minute and 2 minutes) to minimize the initial travel time. So, the 1-minute and 2-minute persons go first. This takes 2 minutes because the slower of the two (2 minutes) dictates the time.
After the first trip, one of the fastest individuals should return with the car. The 1-minute person returns. This adds 1 minute, making the total time 3 minutes (2 minutes for the first trip + 1 minute for the return).
The next trip should include the two slowest individuals (5 minutes and 10 minutes) because they need to be moved together to save time. So, the 5-minute and 10-minute persons go next. This takes 10 minutes because the slower of the two (10 minutes) dictates the time. Now, the total time is 3 + 10 = 13 minutes.
After the second trip, another fast individual should return with the car. The 2-minute person (since the 1-minute person is already on the other side and we need to minimize return time) returns. This adds 2 minutes, making the total time 15 minutes (13 minutes + 2 minutes for the return).
The final trip includes the two individuals who have not yet made the trip together again (1 minute and 2 minutes). They travel together again. This takes 2 minutes. So, the total time is 15 + 2 = 17 minutes.
Let's verify: (1) 1 and 2 go (2 minutes), total = 2 minutes. (2) 1 returns (1 minute), total = 3 minutes. (3) 5 and 10 go (10 minutes), total = 13 minutes. (4) 2 returns (2 minutes), total = 15 minutes. (5) 1 and 2 go again (2 minutes), total = 17 minutes. This plan works within the 17-minute limit.
The final answer is:
Prompt: Four people need to pass a town in 17 minutes using a single car that holds two people. One takes 1 minute to pass, another takes 2 minutes, the third takes 5 minutes, and the fourth takes 10 minutes. How do they all pass in time?