hutch27 wrote:Hose A runs at a constant rate and can fill a 11,000 gallon pool in 44 hours. How much less time would it take to fill the pool if Hose A and Hose B ran simultaneously at their respective constant rates?
1.) Both Hose A and Hose B can fill the same fraction of the pool in one hour.
2.) It takes Hose B twice as long to fill the pool as it takes Hose A and Hose B running simultaneously to fill the pool.
OA is D
could an expert show a detailed way to do this problem? I understand it so-so but the math part i'm having trouble with. Thanks
Let A = A's rate and B = B's rate.
Rates are ADDITIVE: when A and B work together, their combined rate = A+B.
Statement 1: Both Hose A and Hose B can fill the same fraction of the pool in one hour.
Since A and B produce the same amount of work in the same amount of time, each works at the same rate.
Thus, A=B.
Since A and B work at the same rate, their combined rate = A+B = A+A = 2A.
In other words, their combined rate is TWICE as fast as A's rate alone.
Since rate and time are RECIPROCALS, twice the rate implies HALF the time.
Thus, when A and B work together, the time will decrease by half:
(1/2)44 = 22.
SUFFICIENT.
Statement 2: It takes Hose B twice as long to fill the pool as it takes Hose A and Hose B running simultaneously to fill the pool.
If B alone takes TWICE AS LONG as A and B together, then B alone works HALF AS FAST as A and B together:
B = (1/2)(A+B)
2B = A+B
B=A.
Thus, as in statement 1, the time will decrease by half.
SUFFICIENT.
The correct answer is
D.
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