Pumping the Pool?

Question

it takes A 2 hours less time than pump B to empty a certain swimming pool. pump A is started at 8:00. A.M, and pump B is started at 11:00 A.M. If the pool is still half full at 5:00 P.M., then how long would it take pump A working alone ?

Answer 1

Hi,

The general formula is:

time...........time
together....together
-----------.+.------------ = 1, if they did one complete job
time for......time for
A alone......B alone

In your case since it takes pump A 2 hours less time to pump out the pool than pump B, let x = pump B's time alone and x - 2 = pump A's time alone. Since they are only doing half the job, the total will only be ½. The equation so far is:

time...........time
working....working
-----------.+.------------ = ½
x - 2...............x

Since pump A ran from 8 AM until 5 PM, it ran 9 hours. Pump B was on from 11 until 5, so it ran 6 hours. The equation becomes:

...9.........6.......1
------.+.-----.=.---
x - 2.......x.......2

To eliminate the fractions multiply each term by the LCD of 2x(x-2). Once simplified, the problem becomes:

9(2x) + 6(2)(x-2) = 1(x)(x-2)

This solves as follows:

18x + 12x - 24 = x² - 2x

x² -32x + 24 = 0
..........______
-b ± √b² - 4ac
-------------------- = x
........2a

................____________
-(-32) ± √(-32)² - 4(1)(24)
----------------------------------- = x
...........2(1)

.................___
.......32 ± √928
.x.=.--------------- = (32 + 30.46)/2 = 31.23
...........2

It would take pump A 31.23 hours working alone to empty the pool.

I hope that helps!! :-)

Answer 2

Suppose the time in hours of pump A to empty the pool is h.
So the time in hours of pump B is h+2
In one hour the pump A empties 1/h and the pump B 1/h+2
from 8.00 AM to 5pm there are 9 hours. so pump A has removed a fraction 9/h . for pump B from11 am to 17 pm there are 6 hours and B has removed 6/h+2
at 5 pm the pool is 1/2 full
so 1/2 = 9/h+6/(h+2) =(9h+18+6h)/h/(h+2)= 15h+18/h(h+2)
30h +36 = h^2+2h
h^2-28h-36 =0

you find h= 29.5 hours

Answer 3

let pump A take x hours to empty.
In 1 hour it empties 1/x swimming pool

Pump B takes x+2 hours to empty
In 1 hour it empties 1/(x+2) swimming pool

Pump A started at 8:00 AM
Pump B Started at 11:00 AM
Both of them run upto 5:00 PM

In first 3 hours Pump A emptied (1/x)*3 = 3/x swimming pool
In next 6 hours Pump A & B emptied (1/x)*6 + (1/(x+2))*6)
= (6/x) + (6/(x+2))

Total emptied = (3/x) + (6/x) + (6/(x+2)) = 1/2
(3(x+2) + 6(x+2) + 6x) / (x(x+2)) = 1/2
(3x + 6 + 6x + 12 + 6x) /(x^2 + 2x) = 1/2
(15x + 18) / (x^2+2x) = 1/2
2(15x+ 18) = x^2 + 2x
30x + 36 = x^2 + 2x
x^2 +2x - 30x -36 = 0
x^2 - 28x -36 = 0
x= 26.64 or 1.18 hours

Answer 4

let x be the time pump B clears the pool.
then the time for pump A is x-2.

B is working for 6 hrs... A for 9 hrs...
6/x + 9/(x-2) = 1/2

§
12(x-2) + 18x = x^2 - 2x ...
x^2 - 32x + 24 = 0
x^2 - 32x + 16^2 = 16^2 - 24
(x-16)^2 = 232
x = 16 + √232 ... the negative is not possible due to 'x-2'
then pump A needs: 14 + √232 hours.

Answer 5

in case you do not have a three way try equipment ( Cl, pH, TA) then take a pattern of your water into the community pool shop for a loose try. i will guess a case of beer which you're basically utilising a pH and Cl try equipment. TA (entire alkalinity) is particularly between the main needed issues to objective for. If the TA isn't in it is suitable selection of 80-one hundred twenty then you definately can sell off as plenty chlorine as you like in there and little will take place. entire alkalinity governs how your pH sits. If it is no longer precise, your pH is genuinely no longer precise. in the journey that your pH isn't precise your chlorine and maximum different chemical compounds like clarifier won't be able to artwork precise. once you have your TA in selection, your chlorine will start to artwork for you. Backwash that clear out ( or sparkling it if this is a cartridge) on a on an accepted basis foundation till the golf green or murkiness is long previous. If it replaced into so green you're able to desire to no longer see the backside this might take in to each week. interior the advise time, shop your Cl up at 3.0 and don't enable it slip down because it is going to try this as this is used up against the organics interior the pool. additionally, in case you insist on utilising liquid chlorine, use it at dusk. No photograph voltaic ability that UV rays won't knock the chlorine out of the water as quickly and supply it longer to artwork. If the pool shop advise you utilize clarifier, do it, yet get the water chemistry below administration first and shop on with the learning on the bottle.