Data Sufficiency

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

No math is required if you understand that the problem can be solved if we know the rate of B and we can find that from both the statements.

So, both statements are individually sufficient.

Answer : D

If you still need the maths, here you go.
In one hour, hose A will fill 1/44 of the pool.

Statement 1 : B will also fill 1/44 of the pool in one hour.
So, in one hour, together A and B will fill 2/44 = 1/22 of the pool.
So, together A and B will take 22 hours to fill the pool.
So, (44 - 22) = 22 more hours is needed.
Sufficient


Statement 2 : let us assume B takes 2N hours to fill the pool.
So, A and B together take N hours to fill the pool.
In one hour, B alone fills 1/2N of the pool, and A and B together fills 1/N of the pool.
So, 1/44 + 1/N = 1/2N
S0, 1/N = 1/44
The rest is same as statement 1.
Sufficient

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

From 1) If both are filling the same fraction of the tank than it means that both are running at the same rate. So if they run together they can fill the tank in half the time taken by Hose A ie 22 hours.SUFFICIENT

2)This is giving you the same information as above. If the Hose B takes double the time taken by Hose A and Hose B together than Hose A and Hose B must be running at the same speed.SUFFICIENT.

ANSWER D.

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.