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)4/7
b)1/3
c)2/3
d)3/4
E)4/3




Ans B.
Can you please show algebraically how this works using the w=rt formula.
thanks.

Hi TJ,

When multiple objects are performing work at the same time, you add their rates to find the total rate. So if four pumps are filling a tank, their total rate is the sum of all their individual rates.

Let's set the big pump equal to rate p.
So the rate of each small pump = (2/3)p

The sum of all four pumps is p + (2/3)p + (2/3)p + (2/3)p = 3p

So together, the four pumps work 3 times as fast as the original pump. The original equation in w = rt format is W = (p)t, where p is just the big pump.

In order to make the equation balance with our new rate (3p), we must adjust the time as follows: W = (3p)(t/3). The 3s cancel and we have our original equation W = (p)t. So the new time is 1/3 the original time required. B is the answer.

Hope this helps!