Answer:
The correct option is B) 12.
Step-by-step explanation:
Consider the provided information.
Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours.
As we know: [tex]rate =\dfrac{ work}{time}[/tex],
The rate of pump X is [tex]\frac{\frac{1}{4}}{2} = \frac{1}{8}[/tex]
[tex]\frac{1}{4}[/tex] of the water is pumped out of the tank, that means only [tex]\frac{3}{4}[/tex] is left to be pumped out.
All 3 pumps pumped out the remaining [tex]\frac{3}{4}[/tex] of the water out in 3 hours.
The combined rate of all three pumps is: [tex]\frac{\frac{3}{4}}{3} = \frac{1}{4}[/tex]
Pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water.
The rate of pump Y = [tex]\frac{\frac{3}{4}}{18} = \frac{1}{24}[/tex]
Let z is the time taken by pump Z, then the rate of pump Z is [tex]\frac{1}{z}[/tex].
Therefore,
[tex]\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{z}=\dfrac{1}{4}[/tex]
Multiplying both sides by 24 z.
[tex]3z + z + 24 = 6z\\24 = 2z\\12 = z[/tex]
Hence, the correct option is B) 12.
