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Question 696385: two taps A and B together fill a swimming pool i 15 days . Tap A and B are kept open for 12 days and then tap B is closed . It takes another 8 days for the swimming pool to be filled. How many days each tap require to fill the swimming pool
Found 2 solutions by stanbon, ptaylor: Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! two taps A and B together fill a swimming pool i 15 days . Tap A and B are kept open for 12 days and then tap B is closed . It takes another 8 days for the swimming pool to be filled. How many days each tap require to fill the swimming pool
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Let A and B be the rates of the 2 taps.
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Equation:
15A + 15B = 1 job
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20A + 12B = 1 job
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Multiply thru the top equation by 12
multiply thru the bottom equation by 15
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180A + 180B = 12
300A + 180B = 15
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Subtract and solve for A
120A = 3
A = 1/40 job/day (A's rate)
A would take 40 days to fill the pool alone.
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Solve for "B"
20A + 12B = 1
1/2 + 12B = 1
12B = 1/2
B = 1/24 job/day (B's rate)
A would take 24 days to fill the pool alone.
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Cheers,
Stan H.
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Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website! Let x=number of days it takes tap A to fill the pool
Then tap A fills at the rate of 1/x of the pool per day.
Let y=number of days it takes tap B to fill the pool
Then tap B fills at the rate of 1/y of the pool per day
Taps A and B, together, fill the pool at the rate of 1/15 pool per day
so:
1/x + 1/y =1/15-----------------eq1
In 12 days, taps A and B together fill (1/15)*12 =12/15 of the pool
In 8 days, tap A fills (1/x)*8=8/x of the pool
so:
12/15+8/x=1 (1 filled pool, that is)----eq2
Solve eq2, and substitute into eq1
12/15+8/x=1 multiply each term by 15x
12x+120=15x
3x=120
x=40 days-----------------time it takes tap A to fill the pool
From eq1
1/40+1/y=1/15 multiply each term by 120y
3y+120=8y
5y=120
y=24 days---------------time it takes tap B to fill the pool
CK
In 15 days, tap A fills (1/40)*15=15/40=3/8 of the pool
In 15 days, tap B fills (1/24)*15=15/24=5/8 of the pool
3/8+5/8=1 (1 filled pool, that is)
Hope this helps---ptaylor
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