Three pumps begin draining a 7500-gallon pool. At the same time, two pumps begin to drain a 4800-gallon pool. Assuming that all pumps drain at the same time., how many gallons are left in the larger pool when the smaller pool finished being drained?
(a) 300
(b) 600
(c) 900
(d) 1200
To solve this problem, we need to calculate the rate at which the pumps drain the pools and then determine how long it takes for the smaller pool to be drained completely.
Let's start with the rate at which each pump drains the pools. We know that three pumps drain a 7500-gallon pool, so each pump drains 7500/3 = 2500 gallons per pool.
For the smaller pool, we have two pumps draining a 4800-gallon pool, so each pump drains 4800/2 = 2400 gallons per pool.
Now let's calculate the time it takes for the smaller pool to be drained completely. We divide the total number of gallons in the pool (4800) by the rate at which each pump drains the pool (2400).
Time = Total gallons / Rate per pump
Time = 4800 / 2400
Time = 2 hours
Therefore, it takes 2 hours for the smaller pool to be drained completely.
Since all pumps drain at the same time, we can say that in 2 hours, the larger pool also has 2 hours left to be drained.
Now, let's calculate the number of gallons left in the larger pool after 2 hours. Each pump drains at a rate of 2500 gallons per pool, so in 2 hours, each pump will drain 2500 * 2 = 5000 gallons.
Therefore, the larger pool will have 7500 - 5000 = 2500 gallons left after 2 hours.
So, the correct answer is (a) 300.
To solve this problem, we need to find the rate at which each pump drains the pool, and then figure out the time it takes for each pool to be drained.
First, let's find the rate at which each pump drains. Let's assume that each pump drains at a rate of R gallons per hour.
The three pumps draining the larger pool have a combined rate of 3R gallons per hour.
The two pumps draining the smaller pool have a combined rate of 2R gallons per hour.
Now, let's find the time it takes for each pool to be drained.
The larger pool has a volume of 7500 gallons, so it will take 7500 / (3R) hours for it to be drained.
The smaller pool has a volume of 4800 gallons, so it will take 4800 / (2R) hours for it to be drained.
Since we assume that all pumps drain at the same time, the small pool will be drained first. Therefore, we need to find the time it takes for the small pool to be drained.
4800 / (2R) = 2400 / R hours
Now we can determine how many gallons are left in the larger pool when the smaller pool is drained.
The larger pool will have been draining for 2400 / R hours by the time the small pool is drained. So the remaining gallons in the larger pool will be:
7500 - (2400 / R) * (3R) = 7500 - 7200 = 300 gallons
Therefore, the answer is (a) 300 gallons.