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Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours. Then pumps Y and Z started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump Z, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
  • a)
    6
  • b)
    12
  • c)
    15
  • d)
    18
  • e)
    24
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Working alone at its constant rate, pump X pumped out ¼ of the ...
Rate of pump X = 1/8
3 hours are required to pump out the remaining (3/4)ths of tank → 1 hr to pump out 1/4
Rate of X + Rate of Y + Rate of Z = 1/4
Rate of Y + Rate of Z = 1/4 - 1/8 = 1/8
Y takes 18 hours to pump out the remaining (3/4)ths of tank → 6 hrs per (1/4)ths → 24 hrs to pump out fully.
Rate of Y = 1/24
1/24 + Rate of Z = 1/8
Rate of Z = 1/8 - 1/24 = 1/12
Time required to pump out all the water by Z = 12 hrs.
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Community Answer
Working alone at its constant rate, pump X pumped out ¼ of the ...
Let's break down the information provided in the question:

- Pump X pumped out 1/4 of the water in the tank in 2 hours
- Pumps Y and Z, along with Pump X, pumped out the remaining water in 3 hours
- Pump Y alone would have taken 18 hours to pump out the remaining water

We need to find out how long it would take Pump Z to pump out all the water from the tank. Let's calculate the rates of each pump:

- Pump X's rate = 1/4 of the tank in 2 hours = 1/8 of the tank per hour
- Pumps X, Y, and Z combined rate = 3/4 of the tank in 3 hours = 1/4 of the tank per hour
- Pump Y's rate = 1/4 of the tank in 18 hours = 1/72 of the tank per hour

Now, we can find Pump Z's rate by subtracting Pump Y's rate from the combined rate:

Pump Z's rate = Combined rate - Pump Y's rate
Pump Z's rate = 1/4 - 1/72 = 17/72 of the tank per hour

To find out how long Pump Z would take to pump out all the water, we need to divide the total tank capacity by Pump Z's rate:

Time taken by Pump Z = 1 / (17/72) = 72/17 ≈ 4.24 hours

Therefore, Pump Z would take approximately 4.24 hours to pump out all of the water from the tank, which is closest to option B (12 hours).
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Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours. Then pumps Y and Z started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump Z, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?a)6b)12c)15d)18e)24Correct answer is option 'B'. Can you explain this answer?
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