Verified answer

Let x be the total pool water.

Pump A fills 1/2 the pool in an hour (1/2x)

pump B fills 1/3 the pool in an hour (1/3x)

and Pump C empties 2/3 of the pool in and hour.

set up your equation:

1 = (1/2)x + (1/3)x - (2/3)x

solve for x.

Just use some ratios to solve the problem.

pump 1 = 1 pool/2 hours

pump 2 = 1 pool/3 hours

pump 3 = 1 pool/1.33 hours

Let T be the time it takes all 3 pumps to fill the pool.

1 pool = T hours(1 pool/2 hours) + T hours(1 pool/3 hours) + T hours(1 pool/1.33 hours)

1 = T/2 + T/3 + T/1.33

6(1) = 6(T/2 + T/3 + T/1.33)

6= 3T + 2T + 8T

6 = 13T

T = 0.46 hours = 28 minutes.

Answer is 6 hours.

Let capacity be V

Speed of 1 pump (volume/hour) = V/2

Speed of 2 pump = V/3

Speed of 3 pump = -V/(1.5) = -2V/3 [ -ve sign indicates that it draws out water]

Let total time taken be t to fill the tanks if all are used

Then,

t * (V/2 + V/3 -2V/3) = V

t * (1/6) =1

t = 6 hours