after10 min., the hole in the tank gets larger, water leaks out of the tank at 12 gal.per min. an hour after the tank started leaking its empty they fill it up at rate of 6 gal/min for 1st 20 min, then rate of 15 gal/min for 30 min, make a graph W(t)
I would graph this, but it would take too much time. What you would do is basically do a graph with time in minutes on the X axis and the number of gallons in the Y axis. If the tank was empty after 60 minutes, emptying out at a rate of 12 gal/min, then it's safe to assume that the tank started off with 720 gallons since 60 X 12 = 720. At time 0 mins, we are at 720 gallons.
Each minute after that we have 12 gallons less than we originally did until we are empty at 60 minutes.
After that we would have 6 more gallons than we did the previous minute for the next 20 minutes until we reach 120 gallons at 80 minutes.
Then the tank grows by 30 gallons every minute for the next 30 minutes.
Simply add and subtract how many gallons the tank is growing or shrinking every minute to get your Y values for the graph and the points.