Jcpenny wrote:
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and \(1\frac{1}{4}\) hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?
A. \(2\frac{1}{3}\)
B. \(2\frac{2}{3}\)
C. 3
D. \(3\frac{1}{2}\)
E. \(3\frac{2}{3}\)
For this type of question, I like to assign a "nice value" to the job.
In this case we're looking for a number that works well with 1/3, 3/4 and even 1 1/4
So, let's say the pool has a capacity of
60 liters.
At noon the pool was 1/3 full, . . . 1/3 of
60 liters = 20 liters
So, at 12:00pm, the pool contained 20 liters of water
. . . and 1 1/4 hours later it was 3/4 full. 1 1/4 hours = 1.25 hours = 75 minutes.
3/4 of
60 liters = 45 liters
So, at 1:15pm, the pool contained 45 liters of water
What was the total number of hours that it took the pump to fill the pool?45 liters - 20 liters = 25 liters
So, in 1.25 hours, 25 liters of water was added to the pool
Rate = output/timeSo, the rate at which water is added to the pool = (25 liters)/(1.25 hours) =
20 liters per hour Time = output/rateSo, at a rate of
20 liters per hour, the time it takes to fill the
60 liter pool =
60/
20 liters =
3 hoursAnswer: C
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