The objective is to determine the total duration to fill a tank when additional taps are introduced after the tank reaches its halfway mark. The process is detailed below:
1. Initial Fill Phase: A single tap fills the tank in 6 hours. Consequently, one tap fills 1/6 of the tank per hour.
2. First Half Completion: To fill half the tank, the single tap requires 6 / 2 = 3 hours.
3. Additional Taps Introduction: Upon reaching the halfway point, three more identical taps are activated, resulting in a total of 4 taps working on the remaining half.
4. Combined Taps Performance: With 4 taps operational, the collective filling rate per hour is 4 * (1/6) = 4/6 = 2/3 of the tank per hour.
5. Second Half Completion Time: The time needed for the 4 taps to fill the remaining 1/2 of the tank is (1/2) / (2/3) = 3/4 hours.
6. Total Time Calculation: The overall time to fill the tank is the sum of the time for the first half and the time for the second half: 3 + 3/4 = 15/4 = 3.75 hours.
7. Time Conversion: 0.75 hours is equal to 45 minutes.
Therefore, the complete filling time is 3 hours and 45 minutes. This corresponds to the option: 3 hours 45 minutes.
A box contains 16 red, 12 white, and 15 yellow identical marbles. A man picks one marble at a time without replacement. How many times must he pick a marble to be 100% certain of picking at least 3 white marbles?