First, we find out how many quarts of water is in a swimming pool, so we do the following:

And since we know the heart pumps 5 quarts of blood per 60 seconds, and there is a total of 260000 quarts to pump, we can find the amount of time it takes to pump the blood by doing the following:

so now we know that it takes 3120000 seconds to pump the blood. All that is left is find out how many weeks is equal to 3120000 seconds, so we do the following:

So the answer is approximately
5.16 weeks