Working at a constant rate, a certain hose can fill a pool in 10 minutes. Working at a different constant rate, another hose can fill the same pool in 15 minutes. If the two hoses work together but independently to fill the pool after it is half full, how many minutes will it take the hoses to fill the pool?

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Working at a constant rate, a certain hose can fill a pool in 10 minutes. Working at a different constant rate, another hose can fill the same pool in 15 minutes. If the two hoses work together but independently to fill the pool after it is half full, how many minutes will it take the hoses to fill the pool?