math....................?

Question

pipe a can fill a pool in 12 hours pipe b can fill the same pool in 10 hours it take 20 hours to drain the pool if both pipes are working to gether and the drain is left open how long will it take to fill

Answer 1

OK, the RATE of filling or emptying is:
pipe a rate = pool volume / 12 gallons per hour
pipe b rate = pool volume / 10 gallons per hour
pipe d (drain) rate = pool volume / 20 gallons per hour

The fill rate with both A and B is "pool volume/12 + pool volume/10" gallons per hour

The emptying rate is pool volume / 20.
Subtract the emptying rate from the fill rate:
call "pool volume" P

Fill rate with drain open = P/12+P/10-P/20 = P(1/12+1/10-1/20)
= P(5/60+6/60-3/60) = P(8/60)= P(2/15)
So the fill rate is the volume * 1/7.5
So the pool fills in 7.5 hours

Answer 2

1+1=2

Answer 3

rate at which the drain pipe will empty the pool=1/20
rate at which pipes a and b willtogether fill the pool=1/10+1/12
=11/60
the rate at which the pool will be filled when all three pipes are open=11/60-1/20
=11/60-3/60
=8/60
so time taken for filling the pool=60/8=7 1/2 hours

Answer 4

a fills the pool at a rate of 1/12, b fills it at a rate of 1/10, d drains it at a rate of 1/20. So with all open the rate of fill is 1/10 + 1/12 - 1/20 = 6/60 + 5/60 - 3/60 = 8/60, so it will be filled in 60/8 = 7 1/2 hours.

Answer 5

Let's assume the pool has 120 gallons of water.

Pipe A: 120/12=10 gallons per hour
Pipe B: 120/10=12 gallons per hour
Drain: 120/20=6 gallons per hour

Net input: 10+12-6=16 gallons go in per hour
120/16=7.5 hours to fill the pool

Btw very descriptive title you have there =P

Answer 6

rate of filling is x(1/12 +1/10 -1/20)=2x/15, where x=pool volume

so total time = volume/rate = x/2x/15 = 15/2 = 7.5 hour
....



But why such questions ??

Answer 7

x/12 + x/10 - x/20 =1

8x= 60

x = 60/8 ---> 15/2

It will take 15/2 or 7.5 hours to fill the pool.

Answer 8

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Answer 9

1 day or 2 days

Answer 10

all the above answers assume constant flow rates in (OK) and out (not true - the flow rate out is greater if the pool level is higher - the pressure head is greater). if this is strictly an algebra question it's probably a safe assumption. if you are doing fluid mechanics however....