If the water hose was able to fill 1/3 of the pool in 1/2 hour, we can assume that the rate of filling is constant.
Let's first find the fraction of the pool that can be filled in 1 hour. Since the rate of filling is constant, we can multiply the fraction filled in 1/2 hour by 2 to get the fraction filled in 1 hour:
1/3 filled in 1/2 hour x 2 = 2/3 filled in 1 hour
So the hose can fill 2/3 of the pool in 1 hour.
Now we can use this rate to find how long it would take to fill the entire pool. Since the hose can fill 2/3 of the pool in 1 hour, we can set up the following proportion:
2/3 pool filled / 1 hour = 1 pool / x hours
where x is the number of hours it will take to fill the pool.
We can solve for x by cross-multiplying:
2/3 pool filled * x hours = 1 pool * 1 hour
2x/3 = 1
Multiplying both sides by 3/2:
x = 3/2
So it will take 3/2 or 1.5 hours to fill the pool