A small pump can empty a swimming pool in 306 minutes. If two large pumps and a small pump working simultaneously can empty the swimming pool in 68 minutes.

Question

A small pump can empty a swimming pool in 306 minutes. If two large pumps and a small pump working simultaneously can empty the swimming pool in 68 minutes. Find the amount of time one large pump working alone could empty the swimming pool.

Answer 1

First off, let's assume the two large pumps work at the same capacity.

 

The small pump alone does 1/306 parts per minute

If a large pump takes x minutes then it does 1/x parts per minutes.

2 large pumps will do 2/x parts per minutes...

 

The sum of the 2 large pumps and the small pump together do 1/68 parts per minute

 

1/306 + 2/x = 1/68

 

2/x = 1/68 - 1/306

 

2/x = (4.5-1)/306

 

2/x = 3.5/306

 

3.5x = 2(306)

 

x = 2(306)/3.5

 

x = 174.86 minutes for one large pump