A pool has four taps. The first tap takes two days to fill the pool, the second tap three days, the third four days and the last one only 6 hours. How long will it take to fill the pool using all 4 taps at once?

general knowledge math & puzzles

  1. 4 hours 43 minutes and 18 seconds.

  2. 4 hours 50 minutes and 17 seconds.

  3. 3 hours 43 minutes and 17 seconds.

  4. 4 hours 43 minutes and 17 seconds.

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Correct Option: D

AI Explanation

To solve this problem, we can find the rate at which each tap fills the pool by calculating the inverse of the time taken by each tap.

The first tap can fill the pool in 1/2 days, which is equivalent to 1/(2*24) pools per hour. The second tap can fill the pool in 1/3 days, which is equivalent to 1/(3*24) pools per hour. The third tap can fill the pool in 1/4 days, which is equivalent to 1/(4*24) pools per hour. The fourth tap can fill the pool in 6 hours, which is equivalent to 1/6 pools per hour.

To find the combined rate at which all four taps fill the pool, we can add up the rates of each individual tap.

Combined rate = 1/(2*24) + 1/(3*24) + 1/(4*24) + 1/6 pools per hour.

To find the time it takes to fill the pool using all four taps at once, we can take the reciprocal of the combined rate.

Time = 1 / (1/(2*24) + 1/(3*24) + 1/(4*24) + 1/6) hours.

Simplifying the expression, we get:

Time = 4.716667 hours.

Converting this to hours, minutes, and seconds, we have:

Time = 4 hours 43 minutes and 17 seconds.

Therefore, the correct answer is option D) 4 hours 43 minutes and 17 seconds.

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