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Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If Hose A works alone for one hour and then Hose B joins after that, how long will it take in total for the pool to be filled?
  • a)
    2 hours
  • b)
    2 hours, 12 minutes
  • c)
    2 hours, 48 minutes
  • d)
    3 hours
  • e)
    3 hours, 12 minutes
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two hoses (A and B) are filling a pool. Working alone at their individ...
Understanding the Problem
To solve the problem, we need to find out how much of the pool is filled by Hose A and then how much is filled when both hoses work together.
Rates of the Hoses
- Hose A can fill the pool in 6 hours.
- Rate of Hose A = 1/6 of the pool per hour.
- Hose B can fill the pool in 4 hours.
- Rate of Hose B = 1/4 of the pool per hour.
Step 1: Hose A's Contribution
- When Hose A works alone for 1 hour:
- Amount filled = Rate of Hose A × Time = (1/6) × 1 = 1/6 of the pool.
Step 2: Remaining Water to be Filled
- Remaining amount of the pool = 1 - 1/6 = 5/6 of the pool.
Step 3: Combined Rates of Hoses A and B
- When both hoses work together, their combined rate:
- Combined Rate = Rate of Hose A + Rate of Hose B = (1/6 + 1/4).
- Finding a common denominator (12):
- (1/6 = 2/12) and (1/4 = 3/12).
- Combined Rate = 2/12 + 3/12 = 5/12 of the pool per hour.
Step 4: Time to Fill Remaining Pool
- Time needed to fill the remaining 5/6 of the pool:
- Time = Remaining Amount / Combined Rate = (5/6) / (5/12) = (5/6) × (12/5) = 2 hours.
Step 5: Total Time
- Total time = 1 hour (A alone) + 2 hours (A and B together) = 3 hours.
Thus, the correct answer is option D) 3 hours.
Free Test
Community Answer
Two hoses (A and B) are filling a pool. Working alone at their individ...
The Pool has a capacity of 12 units, with Hose A having an efficiency of 2 units per hour and Hose B having an efficiency of 3 units per hour.
After 1 hour, Hose A completes 2 units of work, leaving 10 units remaining.
The combined efficiency of Hose A and Hose B is 5 units per hour.
To fill the remaining 10 units, it will take 10/5 = 2 hours.
Therefore, the total time required to fill the Pool is 1 hour (from Hose A) + 2 hours (to fill the remaining 10 units) = 3 hours. Thus, the answer is (D).
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Two hoses (A and B) are filling a pool. Working alone at their individual constant rates Hose A could fill the pool in 6 hours, and Hose B could do it in 4 hours. If Hose A works alone for one hour and then Hose B joins after that, how long will it take in total for the pool to be filled?a)2 hoursb)2 hours, 12 minutesc)2 hours, 48 minutesd)3 hourse)3 hours, 12 minutesCorrect answer is option 'D'. Can you explain this answer?
Question Description
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