Two pumps of varying power help to fill a tank, after four hours, one breaks down.

Question

An 8 horsepower pump can fill a tank in 8 hours. A smaller, 3 horsepower pump fills the same tank in 12 hours. The pumps are used together to begin filling the tank. After four hours, the 8 horsepower pump breaks down. How long will it take the smaller pump to fill the tank?

 

Answer 1

After the first 4 hours

the fast pump has filled 4/8, or 1/2

and the slow pump has filled 4/12, or 1/3

1- 1/2 - 1/3

1/6 of the tank needs to be filled

 

The slow pump would need 2 hours (2/12 = 1/6). 

Answer 2

 

The 8-horsepower (hp) pump takes 8 hours to fill the tank,

while the 3-hp one takes 12 hours to do the same.

 

So, during the first 4 hours, the 8-hp pump can fill a half of the tank,

while the 3-hp one can fill a third of the tank.

 

So, in 4 hours when the 8-hp pump broke down,

we still have a sixth to go to fill the tank up, i.e., 1 - (1/2) - (1/3) = 1/6.

 

As the 3-hp pump takes 12 hours to fill the tank up,

it will take 2 hours to fill the rest (1/6) of the tank.

 

So, the answer is

"it will take 2 more hours for the smaller pump to fill the tank up

 after the 8-horsepower pump broke down."