Final answer:
When considering both the pool's fill rate and leak rate, it will take 7.5 hours to fill the swimming pool, taking into account the net filling rate after subtracting the leak rate.
Step-by-step explanation:
To solve the real-world problem of how long it will take to fill a swimming pool with a leak, we can utilize a concept known as rates. In this problem, we have two rates: one at which the pool fills and another at which it leaks. The rate of filling the pool is one pool per 6 hours, and the rate of the leak is one pool per 30 hours. The question boils down to finding the net rate at which the pool fills, considering both the filling and leaking rates.
Firstly, let's understand how we express rates. A rate of filling one pool in 6 hours is equivalent to 1/6 of the pool per hour. Similarly, the leaking rate is 1/30 of the pool per hour. To find the net rate at which the pool fills, we subtract the leak rate from the fill rate, which gives us:
Net filling rate = Fill rate - Leak rate
Net filling rate = (1/6 - 1/30) pools per hour
To find a common denominator, we can multiply both fractions by 5/5 and 1/1 respectively:
Net filling rate = (5/30 - 1/30) pools per hour
Net filling rate = 4/30 pools per hour
To find the reciprocal of the net rate which is the total time taken to fill the pool, we calculate:
Time to fill the pool = 1 / Net filling rate
Time to fill the pool = 1 / (4/30) hours
Time to fill the pool = 30 / 4 hours
Time to fill the pool = 7.5 hours
Thus, when considering the leak, it will take 7.5 hours to fill the swimming pool.