A group of 3 small pumps and 1 large pump is filling a tank. Each of the 3 small pumps works at 2/3 of the rate of the large pump. If all 4 pumps work at the same time, they will fill the tank in what fraction of the time that it would have taken the large pump had it operated alone?
A. 1/6 B. 1/3 C. 2/3 D. 3/4 E. 4/3
(B) Since each of the small pumps does 2/3 as much work as the large pump, the 3 small pumps will work at a rate of 3 × 2/3 = 2 times as fast as the large pump.
So the large pump and the 3 small pumps combined can pump 3 times as much as the large pump could by itself.
Therefore, they will finish the job in 1/3 the time it would take the large pump to do the job by itself.
The correct answer is choice (B). ---------- need more explanation .. very confused
If the large pump works at a rate of x ft³/minute, for example, then one of the small pumps works at (2/3)x ft³/minute and all the three small pumps pour 2x ft³/minute.
The small pumps and the large pump combined have a rate of 2x + x = 3x ft³/minute. In other words they work 3 times "faster" than the large pump alone, which means they will fill the same volume 3 times faster.
For example, if the large pump fills the tank in 1 hour, then the large and the three small pumps together will fill it in 1/3 hour.
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