Fergus Castle is a tourist attraction on a small island off the coast of the mainland. A ferry
service runs between the mainland and the island, and takes 40 minutes to make a single
journey in either direction. There is a turnaround time of 5 minutes at the end of each single
journey. Each day, ferries leave the mainland every 20 minutes, at 5, 25 and 45 minutes past
each hour, starting at 09:05. Ferries leave the island at 15, 35 and 55 minutes past each hour,
starting at 09:15.
What is the minimum number of boats needed?
How do I solve this? I have no idea. Thank you so much in advance.
Well, it seems like you're in a bit of a boatload of confusion! But fear not, for Clown Bot is here to give you a humorous helping hand.
To solve this conundrum, let me break it down for you. We know that the ferry service takes 40 minutes to make a single journey, with a 5-minute turnaround time. This means that each round trip takes a total of 45 minutes.
Now let's focus on the departure times. The ferries leave the mainland every 20 minutes, starting at 09:05. So, we have departures at 09:05, 09:25, 09:45, and so on.
On the other hand (or should I say, island?), the ferries leave the island at 15, 35, and 55 minutes past each hour, starting at 09:15. So, island departures occur at 09:15, 09:35, 09:55, and so forth.
To figure out the minimum number of boats needed, we have to consider a scenario where there's maximum demand for both the mainland and the island.
Let's suppose that at 09:05, the first ferry leaves the mainland. By the time it arrives at the island, the next ferry is already waiting to return. So, to make sure there's always a ferry available on both sides, we need at least two boats.
Now, what would happen if we had only two boats? Well, as the second boat leaves the mainland at 09:25, it would arrive at the island just in time to catch the 09:35 island departure. Perfect timing!
But wait a minute, there's a twist! If we only had two boats, the second boat would have to wait for the 09:55 island departure, causing a delay in the schedule. And nobody likes waiting for a delayed boat!
So, to avoid any delays and keep things running smoothly, we need at least three boats in this situation.
So there you have it! The minimum number of boats needed is three. And remember, with Clown Bot guiding you, you'll never be lost at sea... or on an island!
Now, it's time for me to sail away. Good luck with your calculations!
To determine the minimum number of boats needed, we need to consider the ferry schedule and the required turnaround time.
1. Calculate the number of ferry departures from the mainland per hour:
- There are 3 departure times per hour (at 5, 25, and 45 minutes past each hour).
- The ferry service operates from 09:05 onwards, so we have 60 minutes - 5 minutes (turnaround time) = 55 minutes for each hour of operation.
- Divide the 55-minute duration by the 20-minute intervals between departures to get the number of departures: 55 / 20 = 2.75 departures per hour (approximated).
2. Calculate the number of ferry departures from the island per hour:
- There are 3 departure times per hour (at 15, 35, and 55 minutes past each hour).
- The ferry service operates from 09:15 onwards, so we have 60 minutes for each hour of operation.
3. Compare the number of departures from the mainland and the number of departures from the island:
- The minimum number of boats needed is determined by the largest number of departures required in one hour.
- In this case, both the mainland and the island require 3 departures each per hour.
4. Calculate the total number of boats needed:
- Take the larger of the two numbers of departures (3).
- Since each boat is used for a single journey, the minimum number of boats needed is equal to the larger number of departures: 3 boats.
Therefore, the minimum number of boats needed is 3.
To solve this problem, we need to analyze the ferry schedule and turnaround time in order to determine the minimum number of boats needed to provide the service. Here's how you can go about solving it:
Step 1: Analyze the ferry schedule:
- The ferry leaves the mainland every 20 minutes.
- The first ferry leaves at 09:05 and the last ferry leaves at 45 minutes past the hour.
- The ferry leaves the island at 15, 35, and 55 minutes past each hour, starting at 09:15.
Step 2: Determine the total time for a single journey:
- The ferry journey duration is 40 minutes.
- There is a 5-minute turnaround time at the end of each journey.
Step 3: Calculate the number of journeys and turnaround time required:
- The ferry journey from mainland to island and back takes 40 minutes + 5 minutes = 45 minutes.
- The ferry journey from island to mainland and back also takes 40 minutes + 5 minutes = 45 minutes.
Step 4: Calculate the number of journeys within each hour:
- There are 60 minutes in an hour.
- The total time required for each journey (including turnaround time) is 45 minutes.
- Divide 60 minutes by 45 minutes to find the number of journeys per hour.
- We get 60 minutes / 45 minutes = 1.33 journeys per hour.
Step 5: Determine the minimum number of boats needed:
- Since we can't have fractional journeys, we need to round up to the nearest whole number.
- To ensure that there is always a boat available, round up the number of journeys to the nearest whole number.
- In this case, we need at least 2 journeys per hour to cover the ferry schedule.
- Therefore, the minimum number of boats needed is 2.
In conclusion, you would need a minimum of 2 boats to maintain the ferry service between the mainland and the island as described in the problem.