1 pool filled in 8 hours and can drain in 14 hours if pipe and drain open together in one time how long will takes filled.

Question

1 pipe can fill a pool in 8 hours. The drain of pool can empty it in 14 hours. With pipe on and drain open at one time how long will take the pool to be filled.

Answer 1

Hi Alfonso.

 

Since we are filling and draining the same pool, it has a constant volume.  If it holds 100 cubic units full, it drains 100 cm units to get empty.   So the volume is constant.  So lets assume that the volume is 100 cubic units.

 

The rate at which the pool fills is 100 cubic units per 8 hours.

The rate at which the pool drains is 100 cubic unites per 14 hours.

 

Or

 

fill rate = 12.5 cu units/hr

drain rate = 7.143 cu units/hr

 

With both the pipe and the drain open, the pool is only ACTUALLY FILLING at the fill rate - the drain rate = 12.5 - 7.143

 

So water is only staying in the pool at a rate of 5.357 cu units/hr.

 

Using our same 100 cubic units, it would take  100 cu units / 5.357 cu units per hour   to fill the pool.

 

100/5.357 = 18.667  or 18 2/3   hours    or   18 hours and 40 minutes.

Answer 2

Time to fill the pool is 8 hours

Time to empty the pool is 14 hours

rate to fill the pool∗time to fill the pool= completed job (pool filled)

(1/8)time=1 

rate to empty the pool∗time to empty the pool=completed job (pool drained)

(1/14)=1

Then:

(1/8)t-(1/14)t=1

LCD=56

56[(1/8)t-(1/14)t=1]

7t-4t=56

3t=56

t=18.67 hours or t=18 hours 40 minutes