Collaboration Problems!

Problem One:

Complete the steps using 20 and 30 as the shipping times

1. Write down how long you think it will take for the ships to meet back up. (Show all work)
2. Click on the Shipping Route Simulator and enter the two times into the simulation.
3. Press Play and test the simulator. Make sure you write down:
   • How many times ship A completed an entire route (hitting the opposite shore and returning)
4. How many times ship B completed an entire route (hitting the opposite shore and returning)
5. Discuss with your partner and write down what you notice about the relationship between
   • The shipping times
   • The time it takes for them to meet back up
   • The times each ship completed an entire route
6. If you didn't calculate their meet up time correctly, look at what you did wrong and fix your work.

Problem Three:

1. Could you create two boat times so that the boats would never return to shore at the same time? (In other words, I'm asking are there any two numbers that will never have a LCM?)
   • Prove it (you must have some work to be able to prove this!)
   • You may also use the simulator above to try and prove.
2. What if you had three boats?
3. What about four?