A rectangular swimming pool is $10$ meters long and $6$ meters wide. It has a depth of $1$ meter at the shallow end, then slopes to a depth of $1\mathrm{.}5$ meters at the deep end, as shown in the following cross section $($not to scale$).$ It is being filled with a hose at a rate of $50,000$ cubic centimeters per minute. $225$ minutes after the hose is turned on$,$ the water is rising at a rate of $\_\_\_\_\_$ cm per second. Round to $3$ decimal places."