Two pirate scouts, from different ships, discover an enormous treasure trove at the same time. The trove is located between the two ships, but the scout from Ship A is only $0.50\text{ km}$ from his ship while the scout from Ship B is $4.00\text{ km}$ from her ship. There are $31500$ pieces of treasure in the trove and each rowboat from ship A can only carry $5.00\times10^2 (500\pm1)$ pieces at a time without sinking. Assume that both scouts start at the treasure trove and return to their ships empty-handed. Ship A has two rowboats and all pirates from Ship A will row with the same constant speed. Ship B has one rowboat and the pirates from Ship B will all row with the same constant speed of $2.0\text{ m/s.}$ If a rowboat from Ship B catches up to a rowboat from Ship A, they will overpower the pirates and capture the treasure! What is the minimum speed at which pirates from Ship A can row in order to prevent the other pirates from stealing any of the loot?

Guest Sep 24, 2022