Since it has been a year, I am not sure if this is still an open problem, but the answer provided here was wrong on several fronts.
The answer provided did not answer the question being asked. The questions states that the water flowing into the tank is doubling and not, as the answer provided solves for, the volume of fluid in the tank. The problem also assumes that the tank starts out empty, and we don't have enough information to determine if that is the case.
So for the tank starting out empty, If the problem stated the amount of fluid in the tank at any time between t=0 and t=60 we would have enough information to solve for the integration constant, but that is not present here. So for example, since we are solving for the rate of water flowing into the tanks a perfectly valid solution to the problem as stated could have the tank start out more than half full. In that case we don't have enough information to find out when the tank was half full. To help visualize that take any solution to the rate problem filling a tank of size A, and it is also a valid solution for a tank of size 2A that starts half full. From that we can see that is is also a solution for tanks of size 3A that start out with 2A fluid in them, or for tanks of size 5/4A that start out with 1/4A of fluid in them. There are an infinite set of solutions. Just picking the integration constant to being zero is convenient, but its an arbitrary choice not supported by the problem.
If we are talking about the volume of fluid in the tank doubling. Then we can solve for the initial volume of fluid in the tank.
Aaron