RSOHAL wrote:
At a constant Rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
A. 10
B. 12
C. 15
D. 25
E. 50
We are given that the large hose takes 20 minutes to fill a swimming pool and that the small hose takes 30 minutes to fill the same swimming pool.
Since rate = work/time, the rate of the large hose is 1/20 and the rate of the small hose is 1/30.
We need to determine the number of minutes, when working simultaneously, it would take both hoses to fill the swimming pool. To solve, we can use the combined worker formula.
work of the large hose + work of the small hose = total work
Since the pool is being filled, the total work completed is 1 job. We can also let the time worked, in minutes, for both hoses, equal the variable t. Using the formula work = rate x time, we express the work of each hose as follows:
work of the large hose = (1/20)t
work of the small hose = (1/30)t
Lastly, we can determine t:
work of the small hose + work of the large hose = 1
(1/20)t + (1/30)t = 1
(3/60)t + (2/60)t = 1
(5/60)t = 1
t = 1/(5/60)
t = 60/5
t = 12
Alternate Solution:
In one minute, the larger hose can fill 1/20 of the pool, and the smaller hose can fill 1/30 of the pool. If they are used simultaneously, they fill 1/20 + 1/30 = 5/60 = 1/12 of the pool in one minute. If they fill 1/12 of the pool in one minute, they will fill 12/12 of the pool in 12 minutes.
Answer: B
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