The Sisyphus monastery is on a hill, and every day donkeys climb the hill carrying water from the well in the valley. There are many donkeys, and they leave the well (at the bottom of the hill) every 15 minutes. They take one hour to climb the hill, 10 minutes to unload their water, and then half an hour to return to the well.

When a donkey goes uphill carrying water in the middle of the day, how many does it pass coming down?

A container ship is overtaking an oil tanker on the way out of Harwich Harbor, and the first mate notices that if he starts walking from the front of the container ship when the two ships start overlapping, he reaches the back as the two ships separate. He walks at 3 km/hour.

If the container ship is 100 m long and traveling at 12 km/hour, how long is the oil tanker?

In the given scenario, the donkeys leave the well every 15 minutes, take one hour to climb the hill, 10 minutes to unload the water, and then half an hour to return to the well. We are asked how many donkeys a donkey passing uphill carrying water encounters when it is in the middle of the day.

Let's break down the time taken by a donkey on its trip:

- Time taken to climb the hill: 1 hour

- Time taken to unload the water: 10 minutes

- Time taken to return to the well: 30 minutes

So, the total time for a donkey's round trip is 1 hour + 10 minutes + 30 minutes = 1 hour and 40 minutes.

Since the donkeys leave the well every 15 minutes, in the span of 1 hour and 40 minutes, there will be 1 hour and 40 minutes / 15 minutes = 6 donkeys leaving the well.

However, we are only interested in the number of donkeys encountered by a donkey going uphill carrying water in the middle of the day. As each donkey takes 1 hour to climb the hill, the donkey going uphill in the middle of the day will encounter half of the 6 donkeys that left the well during its trip.

Therefore, the donkey going uphill carrying water in the middle of the day will pass 6 donkeys / 2 = 3 donkeys coming down.

Now let's move on to the second scenario:

The container ship is overtaking the oil tanker, and the first mate starts walking from the front of the container ship when the two ships start overlapping. He reaches the back of the container ship as the two ships separate. The first mate walks at a speed of 3 km/hour.

Given:

Length of the container ship = 100 m

Speed of the container ship = 12 km/hour

To find the length of the oil tanker, we can set up a proportion based on the relative speeds of the two ships:

Length of container ship / Speed of container ship = Length of oil tanker / Relative speed of the two ships

Converting the speed of the container ship to meters per hour:

Speed of container ship = 12 km/hour * 1000 m/km = 12,000 m/hour

Relative speed of the two ships = Speed of container ship - Speed at which the first mate walks = 12,000 m/hour - 3 km/hour * 1000 m/km = 12,000 m/hour - 3,000 m/hour = 9,000 m/hour

Now we can set up the proportion:

100 m / 12,000 m/hour = Length of oil tanker / 9,000 m/hour

Cross-multiplying:

Length of oil tanker = (100 m * 9,000 m/hour) / 12,000 m/hour

Length of oil tanker = 75 m

Therefore, the length of the oil tanker is 75 meters.