Problem Statement
In this problem we had to figure out how many planes would be needed to ensure the flight of one plane around the world on a great circle. Each airplane can only hold enough fuel to travel half way around the world, any amount of fuel can be transferred from plane to plane. The only source of fuel is on the island.
In this problem we had to figure out how many planes would be needed to ensure the flight of one plane around the world on a great circle. Each airplane can only hold enough fuel to travel half way around the world, any amount of fuel can be transferred from plane to plane. The only source of fuel is on the island.
Process Description
Originally I thought you'd need two planes in order to make one plane travel around the world. I then realized, how
is the other plane going to land on the island? You'd need at least 3 planes in order to make a safe trip around the world with every plane being safe and landing.
Originally I thought you'd need two planes in order to make one plane travel around the world. I then realized, how
is the other plane going to land on the island? You'd need at least 3 planes in order to make a safe trip around the world with every plane being safe and landing.
Solution
The answer to this problem is 3 planes. Planes 1 & 2 & 3 take off together but after a 1/4 of a unit, plane 3 refuels planes 1&2 and returns. Plane 2 fills plane 1's tank after another 1/4 unit and returns. Planes 2 & 3 take off in the opposite direction and at 1/3 way out plane 3 fills plane 2's tank until it is full and then returns. Both planes return to the island and are safe.
The answer to this problem is 3 planes. Planes 1 & 2 & 3 take off together but after a 1/4 of a unit, plane 3 refuels planes 1&2 and returns. Plane 2 fills plane 1's tank after another 1/4 unit and returns. Planes 2 & 3 take off in the opposite direction and at 1/3 way out plane 3 fills plane 2's tank until it is full and then returns. Both planes return to the island and are safe.
Self-Assesment and Reflection
I've done a problem similar before in the past but just with different variants in fuel and instead of planes, boats. I can't say I learned anything new from it but I know that problems like these are important to train the mind to think in a different way from traditional mathematical problems. I think I deserve around an A on this assignment because my group and I got it done quickly and efficiently together. The Habit of Mind that relates closely to this problem is collaboration and listening to what other group members have to say because they can look at it in a different way.
I've done a problem similar before in the past but just with different variants in fuel and instead of planes, boats. I can't say I learned anything new from it but I know that problems like these are important to train the mind to think in a different way from traditional mathematical problems. I think I deserve around an A on this assignment because my group and I got it done quickly and efficiently together. The Habit of Mind that relates closely to this problem is collaboration and listening to what other group members have to say because they can look at it in a different way.