The first tap fills 1/60 of the pool per minute (1/(60*1)).
The second tap fills 1/120 of the pool per minute (1/(60*2))
The third tap fills 1/180 of the pool per minute.
The fourth tap fills 1/240 of the pool per minute.
The formula for a job is Job (usually 1) = rate times time.
The rate is 1/60 + 1/120 + 1/180 + 1/240 = 12/720 + 6/720 + 4/720 + 3/720 = 25/720 = 5/144 of the pool per minute.
1 = 5/144 * t
1 * 144/5 = t = approximately 28.8 minutes, or 28 minutes, 48 seconds.
You can also express the rates as hourly. The first tap fills 1 pool per hour. The second fills 1/2 pool per hour. The third fills 1/3 pool per hour. The fourth fills 1/4 pool per hour. The combined rate is 1 + 1/2 + 1/3 + 1/4 = 12/12 + 6/12 + 4/12 + 3/12 = 25/12 of the pool per hour.
1 = 25/12 * t
12/25 = 5 = .48 hours = 28.8 minutes = 28 minutes, 48 seconds.
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