Pump A alone can empty the city pool in 12 hours. If only pump B is used, it takes 24 hours to empty the pool. How long would it take to drain the pool if both pumps were used together?
A 1/12 pool / hr
B 1/24 pool / hr
together 3/24 pool/hr
so 24/3 = 8 hr/pool
To find out how long it would take to drain the pool if both pumps were used together, we can use the concept of work rates.
Let's denote the rate at which Pump A can empty the pool as A and the rate at which Pump B can empty the pool as B.
We know that Pump A takes 12 hours to empty the pool, so we can write A = 1/12 (since it empties 1 pool per 12 hours). Similarly, Pump B takes 24 hours to empty the pool, so B = 1/24.
Now, if both pumps are working together, their rates would add up. Let's denote the combined rate as C.
C = A + B
Substituting the values of A and B:
C = 1/12 + 1/24
To simplify this equation, find the common denominator, which is 24.
C = (2/24) + (1/24) = 3/24 = 1/8
This means that if both pumps A and B are used together, their combined rate is 1/8, meaning they can empty 1 pool per 8 hours.
Therefore, it would take both pumps together 8 hours to drain the pool.