Dan has decided to create cat hammocks at home. He has to first build the body of the cat hammock then twine the supports together and finally package the final product. Dan can build $1$ cat hammock body every $6$ minutes, have his son twine $1$ support together every $10$ minutes and have his daughter package $1$ finished product every $3$ minutes.

Each week Dan and his family have $10$ hours to make cat hammocks. How many can they complete in $10$ hours $($assuming they've been making cat hammocks in the past weeks already$)?$ Round down to the lower whole number, e$.$g$.,42\mathrm{.}87$ will be reported as $42.$