Can you please help me with these questions

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Jose is going to use a random number generator 500500 times. each time he uses it, he will get a 1, 2, 3,1,2,3, or 44.

Can someone me with #s 8, 9, and 11. with just one of the three also works. prove using only trig identities.