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When three water pumps A, B and C are simultaneously turned

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When three water pumps A, B and C are simultaneously turned

by Max@Math Revolution » Thu Dec 19, 2019 6:09 am
[GMAT math practice question]

When three water pumps A, B and C are simultaneously turned on to fill a water tank, it takes 4 hours, using only A and C it takes 6 hours, and using only B and C it takes 6 hours and 40 minutes. How would it take to fill the water tank with only A, B or C respectively??

A. 12hrs, 8hrs, 15hrs
B. 10hrs, 12hrs, 15hrs
C. 11hrs, 12hrs, 13hrs
D. 10hrs, 11hrs, 14hrs
E. 8hrs, 10hrs, 14hrs
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by deloitte247 » Sun Dec 22, 2019 11:58 am
How long would it take to fill the water tank with only A, B or C respectively?
A+B+C = 4 hours
A+C = 6 hours
B+C = 6.7 hours
in 1 hour,
$$\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{4}\ hours\ \ \ \ ----\ eqn\ \left(1\right)$$
$$\frac{1}{A}+\frac{1}{C}=\frac{1}{6}\ hours\ \ \ \ ----\ eqn\ \left(2\right)$$
$$\frac{1}{B}+\frac{1}{C}=\frac{1}{6.7}\ hours\ \ \ \ ----\ eqn\ \left(3\right)$$
From eqn (2)
$$\frac{1}{A}+\frac{1}{C}=\frac{1}{6}\ hours$$
$$\frac{1}{C}=\frac{1}{6}\ -\frac{1}{A}$$
Substituting this into eqn (1)
$$\frac{1}{A}+\frac{1}{B}+\frac{1}{6}-\frac{1}{A}=\frac{1}{4}$$
$$\frac{1}{B}+\frac{1}{6}=\frac{1}{4}$$
$$\frac{1}{B}=\frac{1}{4}-\frac{1}{6}=\frac{6-4}{24}=\frac{1}{12}$$
$$B=12\ hours$$

From Eqn (3)
$$\frac{1}{B}+\frac{1}{C}=\frac{1}{6.7}\ hours\ \ \ \ ----\ eqn\ \left(3\right)$$
Where 1/B = 1/12
$$\frac{1}{12}+\frac{1}{C}=\frac{1}{6.7}$$
$$\frac{1}{C}=\frac{1}{6.7}-\frac{1}{12}=\frac{12-6.7}{80.4}=\frac{5.3}{80.4}$$
$$C=15.2\ hours$$

From Eqn (2),
$$\frac{1}{A}+\frac{1}{C}=\frac{1}{6}\ hours\ \ \ \ ----\ eqn\ \left(2\right)$$
$$\frac{1}{A}+\frac{1}{15.2}=\frac{1}{6}$$
$$\frac{1}{A}=\frac{1}{6}-\frac{1}{15.2}=\frac{15.2-6}{91.2}=\frac{9.2}{91.2}$$
$$A=9.9\ hours\approx10hours$$
B=12 hours
$$C=15.2\ hours\approx15hours$$

Answer = option B

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by Max@Math Revolution » Sun Dec 22, 2019 5:13 pm
=>

Assume A, B and C are the it takes machines A, B and C to fill the water tank, respectively.
Then we have 1/A + 1/B + 1/C = 1/4, 1/A + 1/B = 1/6 and 1/B + 1/C = 1/{6(2/3)} = 3/20.
When we add the last two equations, we have 1/A + 2/B + 1/C = 19/20.
When we subtract the first equation from the sum of last two equation, we have 1/C = (1/A + 1/B + 2/C) - (1/A + 1/B + 1/C) = 19/60 - 1/4=(19-15)/60=4/60=1/15.
We have 1/A = 1/10 and 1/B = 1/12.
Thus we have A = 10, B = 12 and C = 15.

Therefore, B is the answer.
Answer: B
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by Scott@TargetTestPrep » Wed Jan 01, 2020 6:44 pm
Max@Math Revolution wrote:[GMAT math practice question]

When three water pumps A, B and C are simultaneously turned on to fill a water tank, it takes 4 hours, using only A and C it takes 6 hours, and using only B and C it takes 6 hours and 40 minutes. How would it take to fill the water tank with only A, B or C respectively??

A. 12hrs, 8hrs, 15hrs
B. 10hrs, 12hrs, 15hrs
C. 11hrs, 12hrs, 13hrs
D. 10hrs, 11hrs, 14hrs
E. 8hrs, 10hrs, 14hrs
We can create the equations:

1/A + 1/B + 1/C = ¼

and

1/A + 1/C = â…™

and

1/B + 1/C = 1/(6 + â…”) = 1/(20/3) = 3/20

Subtracting the second equation from the first, we have:

1/B = ¼ - ⅙

1/B = 3/12 - 1/12

1/B = 1/12

B = 12

Subtracting the third equation from the first, we have:

1/A = ¼ - 3/20

1/A = 5/20 - 3/20

1/A = 2/20 = 1/10

A = 10

Since only choice B has A = 10 and B = 12, the correct choice must be B.

Answer: B

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