Hose A can fill a pool in 3 days. Hose B can fill the same pool in 4

Question

Hose A can fill a pool in 3 days. Hose B can fill the same pool in 4 days. How long will it take both hoses working together to fill the pool if hose A stops when the pool is half full?

(A)  \frac{5}{7}  days

(B)  1 \frac{5}{7}  days

(C) 2 days

(D)  2 \frac{6}{7}  days

(E) 3 days

atulayakumar · Answer

Answer will be option D.

Together A&B can fill hose in 12/7 days. To fill half it will take 12/14 days i.e. 6/7 days. Rest half to be filled by B alone so it will take another 2 days hence total days is 2+ 6/7

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LipiSinha · Answer

To fill half the pool, A alone will take 1.5 days and B alone will take 2 days.

So, together they can fill half of the pool in 6/7 days.

Hose A stops when the pool is half full. 
So, B will have to fill half of the pool alone.
If hose B take 4 days to fill a pool, it will take 2 days to fill half the pool.

Therefore, total time taken = 2(6/7) days.

The answer will be D.

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Bunuel · Answer

Veritas Prep Official Explanation

Convert times to rates:

R_A = \frac{1}{3} ;

R_B = \frac{1}{4} ;

R_{COMBINED} = \frac{1}{3} +\frac{1}{4} = \frac{7}{12}

Now you must first calculate how long it takes the two hoses together to fill half of the pool using the Work = Rate x Time formula:

\frac{1}{2} = \frac{7}{12} * Time

Time = \frac{1}{2} (\frac{12}{7}) = \frac{6}{7}  day to fill the first half of the pool

Because conditions change after half of the pool is filled, you should “reset” the equation. For the second half of the pool, you can just use logic. Hose B works alone to fill the second half of the pool, and it takes hose B 4 days to fill an entire pool. Therefore it will take hose B 2 days to fill the second half of the pool. Adding 2 days to the  \frac{6}{7}  day to fill the first half of the pool, you see that it will take  2 \frac{6}{7}  days to fill the pool.  The correct answer choice is D.

MathRevolution · Answer

Hose A can fill a pool in 3 days. Hose B can fill the same pool in 4 days. How long will it take both hoses working together to fill the pool if hose A stops when the pool is half full?

Hose A can fill a pool in 3 days: 1 day:  \frac{1}{3}  work
Hose B can fill a pool in 4 days: 1 day:  \frac{1}{4}  work

Together:  \frac{1}{3}  +  \frac{1}{4}  =  \frac{7}{12}  work

Together days:  \frac{12}{7}

A and B work till half-fill:  \frac{12}{7}  *  \frac{1}{2}  =  \frac{12}{14}  or  \frac{6}{7}  days

Rest half fill was done by B at the rate of  \frac{1}{4}

=>  \frac{1}{2}  work =  \frac{1}{4}  work

=>  \frac{4}{2}  = 2 days

Total days:  \frac{6}{7}  + 2 =  \frac{20}{7}  days

Answer D

Paras96 · Answer

To solve this problem, we can first calculate the rates at which each hose can fill the pool, and then determine how long it takes them to fill half of the pool together when working simultaneously.

Hose A can fill the pool in 3 days, so its rate is 1 pool per 3 days, which we can write as 1/3 pools per day.

Hose B can fill the pool in 4 days, so its rate is 1 pool per 4 days, which we can write as 1/4 pools per day.

Now, when both hoses A and B are working together, their rates add up:

Rate of A + Rate of B = (1/3) + (1/4)

To add these fractions, we need a common denominator, which is 12. So, we rewrite the fractions with a common denominator:

(4/12) + (3/12) = 7/12 pools per day

Now, we know that together, hoses A and B can fill 7/12 of the pool in one day. To fill half of the pool, they need to fill 1/2 of it. We can set up an equation to find out how many days it will take:

(7/12) * D = 1/2

Where D is the number of days it takes to fill half of the pool. Now, solve for D:

D = (1/2) / (7/12)

To divide by a fraction, you can multiply by its reciprocal:

D = (1/2) * (12/7)

D = 6/7 days

So, it will take hoses A and B approximately 2 6/7 days to fill half of the pool when working together.

Hence D

bumpbot · Answer

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Hose A can fill a pool in 3 days. Hose B can fill the same pool in 4

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